[1] D. V., Alekseevskij, E. B., Vinberg and A. S., Solodovnikov, Geometry of Spaces of Constant Curvature, Volume 29 of the series Encyclopaedia of Mathematical Sciences, Springer 1993. See §7.2.
[2] E., Anderson, “Strong coupled relativity without relativity,” Gen. Rel. Grav. 36, 255 (2004) [gr-qc/0205118]. See §6.7.
[3] L., Andersson and A. D., Rendall, “Quiescent cosmological singularities,” Commun. Math. Phys. 218, 479 (2001) [gr-qc/0001047]. See Introduction, §3.2, 4.7, 6.5.4.
[4] D. V., Anosov, Geodesic flows on Closed Riemanian Manifolds of Negative Curvature, Trudy Mat. Inst. Steklova (ed. I. G., Petrovskii), 90 (1967). See §3.2, 5.9, 6.6.
[5] R. L., Arnowitt, S., Deser and C. W., Misner, “Canonical variables for general relativity,” Phys. Rev. 117, 1595 (1960). See §5.1.
[6] A., Ashtekar, A., Henderson and D., Sloan, “Hamiltonian general relativity and the Belinskii, Khalatnikov, Lifshitz conjecture,” Class. Quant. Grav. 26, 052001 (2009) [arXiv:0811.4160 [gr-qc]]. See §2.5.
[7] A., Ashtekar, A., Henderson and D., Sloan, “A Hamiltonian formulation of the BKL conjecture,” Phys. Rev. D 83, 084024 (2011) [arXiv:1102.3474 [gr-qc]]. See §2.5.
[8] J. D., Barrow, “Chaotic behavior in general relativity,” Phys. Rept. 85, 1 (1982). See §3.1, 3.2.
[9] J. D., Barrow and R. A., Matzner, “The homogeneity and isotropy of the universe,” Mon. Not. R. Astr. Soc. 181, 719 (1977). See Preface to §4.8.
[10] X., Bekaert, S., Cnockaert, C., Iazeolla and M. A., Vasiliev, “Nonlinear higher spin theories in various dimensions,” hep-th/0503128, in Proceedings of the first Solvay Workshop on “Higher Spin Gauge Theories,” eds. R., Argurio, G., Barnich, G., Bonelli and M., Grigoriev, Université Libre de Bruxelles – Vrije Universiteit Brussel (2004). See §6.1.
[11] V. A., Belinski, “Turbulence of a gravitational field near a cosmological singularity,” JETP Letters 56, 421 (1992). See §3.3.
[12] V. A., Belinski, “Stabilization of the Friedmann big bang by the shear stresses,” Phys. Rev. D 88, 103521 (2013). See §4.8.1, 4.8.2.
[13] V. A., Belinski, E. S., Nikomarov and I. M., Khalatnikov, “Investigation of the cosmological evolution of viscoelastic matter with causal thermodynamics,” Sov. Phys. JETP 50, 213 (1979). See §4.8.1, 4.8.2.
[14] V. A., Belinski and I. M., Khalatnikov, “On the nature of the singularities in the general solution of the gravitational equations,” Sov. Phys. JETP 29, 911 (1969). See §1.7, 2.1, B.3.
[15] V. A., Belinski and I. M., Khalatnikov, “General solution of the gravitational equations with a physical singularity,” Sov. Phys. JETP 30, 1174 (1970) [Zh. Eksp.Teor. Fiz. 57, 2163 (1969)]. See §4.3.1.
[16] V. A., Belinski and I. M., Khalatnikov, “Effect of scalar and vector fields on the nature of the cosmological singularity,” Sov. Phys. JETP 36, 591 (1973) [Zh. Eksp. Teor. Fiz. 63, 1121 (1972)]. See Introduction, §4.1, 4.3.1, 4.5, C.3.
[17] V. A., Belinski and I. M., Khalatnikov, “On the influence of the spinor and electromagnetic field on the cosmological singularity character,” Rend. Sem. Mat. Univ. Politech. Torino 35, 159 (1977) [preprint of Landau Institute for Theoretical Physics, Chernogolovka 1976]. See §4.1, Preface to App.C.
[18] V. A., Belinski and I. M., Khalatnikov, “On the influence of matter and physical fields upon the nature of cosmological singularities,” Soviet Science (Physics) Reviews, Harwood Acad. Publ. A3, 555 (1981). See Introduction, §4.1, 4.3.1, 4.3.2.
[19] V. A., Belinski, I. M., Khalatnikov and E. M., Lifshitz, “Oscillatory approach to a singular point in the relativistic cosmology,” Adv. in Phys. 19, 525 (1970). See §1.7, 3.1, 4.1.
[20] V. A., Belinski, I. M., Khalatnikov and E. M., Lifshitz, “Construction of a general cosmological solution of the Einstein equations with a time singularity,” Sov. Phys. JETP 35, 838 (1972) [Zh. Eksp.Teor. Fiz. 62, 1606 (1972)]. See §1.9, A.4.
[21] V. A., Belinski, I. M., Khalatnikov and E. M., Lifshitz, “A general solution of the Einstein equations with a time singularity,” Adv. in Phys. 31, 639 (1982). See §1.9, 4.1, A.4.
[22] V. A., Belinski, I. M., Khalatnikov and M. P., Ryan, “The oscillatory regime near the singularity in Bianchi-type IX universes,” preprint (order 469, 1971) of Landau Institute for Theoretical Physics, Moscow 1971 (unpublished); the work due to V. A., Belinski and I. M., Khalatnikov is published as sections 1 and 2 in M. P., Ryan, Ann. Phys. 70, 301 (1971). See §2.4.
[23] B. K., Berger, “Numerical approaches to space-time singularities,” Living Rev. Rel. 5, 1 (2002). See §1.4, 4.7.
[24] B. K., Berger, “Hunting local mixmaster dynamics in spatially inhomogeneous cosmologies,” Class. Quant. Grav. 21, S81 (2004) [gr-qc/0312095]. See §4.7.
[25] B. K., Berger, D., Garfinkle, J., Isenberg, V., Moncrief and M., Weaver, “The singularity in generic gravitational collapse is space-like, local, and oscillatory,” Mod. Phys. Lett. A 13, 1565 (1998) [gr-qc/9805063]. See §4.7.
[26] B. K., Berger and V., Moncrief, “Numerical investigation of cosmological singularities,” Phys. Rev. D 48, 4676 (1993) [gr-qc/9307032]. See §1.4.
[27] E., Bergshoeff, M., de Roo, B., de Wit and P., van Nieuwenhuizen, “Ten-dimensional Maxwell–Einstein supergravity, its currents, and the issue of its auxiliary fields,” Nucl. Phys. B 195, 97 (1982). See §6.1.
[28] O. I., Bogoyavlenskii and S. P., Novikov, “Singularities of the cosmological model of the Bianchi IX type according to the qualitative theory of differential equations,” Sov. Phys. JETP 37, 747 (1973). See §3.2.
[29] N., Bourbaki, Groupes et algèbres de Lie, chapter 4, Eléments de mathématique, Hermann, 1968. See §7.3, 7.4.
[30] P., Breitenlohner and D., Maison, “On the Geroch group,” Ann. Inst. Henri Poincaré 46, 215 (1986). See §7.7.
[31] D., Brill and J. A., Wheeler, “Interaction of neutrinos and gravitational fields,” Rev. Mod. Phys. 29, 465 (1957). See §C.1.
[32] C., Cattaneo, “Sur une forme de l'équation de la chaleur éliminant le paradoxe d'une propagation instantanée,” Comptes rendus Acad. Sci. Paris Sér. A-B 247, 431 (1958). Based on his earlier seminar talk “Sulla conduzione del calore,” Atti Semin. Mat. Fis. Univ. Modena 3, 83 (1948). See §4.8.1.
[33] G. F., Chapline and N. S., Manton, “Unification of Yang–Mills theory and supergravity in ten dimensions,” Phys. Lett. B 120, 105 (1983). See §6.1.
[34] D. F., Chernoff and J. D., Barrow, “Chaos in the mixmaster universe,” Phys. Rev. Lett. 50, 134 (1983). See §3.1, 3.2.
[35] D. M., Chitre, Ph.D. Thesis, University of Maryland (1972). See Introduction, §2.4, 3.2, 6.7.
[36] D., Christodoulou and S., Klainerman, The Global Nonlinear Stability of the Minkowski Space, Princeton Mathematical Series, 41 (1993). See §1.10.
[37] N. J., Cornish and J. J., Levin, “The mixmaster universe is chaotic,” Phys. Rev. Lett. 78, 998 (1997). See §3.1, 3.2.
[38] N. J., Cornish and J. J., Levin, “Mixmaster universe: a chaotic Farey tale,” Phys. Rev. D 55, 7489 (1997). See §3.1, 3.2.
[39] E., Cremmer and B., Julia, “The SO(8) supergravity,” Nucl. Phys. B 159, 141 (1979). See §7.7.
[40] E., Cremmer, B., Julia, H., Lu and C. N., Pope, “Higher-dimensional origin of D = 3 coset symmetries,” arXiv:hep-th/9909099. See §D.9.
[41] E., Cremmer, B., Julia and J., Scherk, “Supergravity theory in 11 dimensions,” Phys. Lett. B 76, 409 (1978). See §6.1, 7.6.2, 7.7.
[42] E., Czuchry, D., Garfinkle, J. R., Klauder and W., Piechocki, “Do spikes persist in a quantum treatment of space-time singularities?” Phys. Rev. D 95, 024014 (2017) [arXiv:1605.04648 [gr-qc]]. See §1.4.
[43] E., Czuchry and W., Piechocki, “Bianchi IX model: reducing phase space,” Phys. Rev. D 87, 084021 (2013) [arXiv:1202.5448 [gr-qc]]. See §2.4.
[44] T., Damour, S., de Buyl, M., Henneaux and C., Schomblond, “Einstein billiards and overextensions of finite dimensional simple Lie algebras,” JHEP 0208 (2002) 030 [hep-th/0206125]. See §7.6.2, 7.6.3, D.9.
[45] T., Damour and M., Henneaux, “Chaos in superstring cosmology,” Phys. Rev. Lett. 85, 920 (2000) [arXiv:hep-th/0003139]. [See also short version in Gen. Rel. Grav. 32, 2339 (2000).] See Introduction, §4.6.2, 6.7.
[46] T., Damour and M., Henneaux, “Oscillatory behaviour in homogeneous string cosmology models,” Phys. Lett. B 488, 108 (2000) [arXiv:hep-th/0006171]. See Introduction, §4.6.2, 6.7, 7.6.2.
[47] T., Damour and M., Henneaux, “E10,BE10 and arithmetical chaos in superstring cosmology,” Phys. Rev. Lett. 86, 4749 (2001) [arXiv:hep-th/0012172]. See Introduction, §5.6, 6.2, 6.7, 7.7.
[48] T., Damour, M., Henneaux, B., Julia and H., Nicolai, “Hyperbolic Kac–Moody algebras and chaos in Kaluza–Klein models,” Phys. Lett. B 509, 323 (2001) [arXiv:hep-th/0103094]. See §5.10.2, 6.7, 7.6.1.
[49] T., Damour, M., Henneaux and H., Nicolai, “E10 and a ‘small tension’ expansion of M theory,” Phys. Rev. Lett. 89, 221601 (2002) [arXiv:hep-th/0207267]. See §7.7.
[50] T., Damour, M., Henneaux and H., Nicolai, “Billiard dynamics of Einstein-matter systems near a spacelike singularity,” in Lectures on Quantum Gravity, Proceedings of the School on Quantum Gravity, Valdivia, Chile, January 4–14, 2002, A., Gomberoff and D., Marolf eds, Series of the Centro de Estudios Científicos, Springer 2005. See §5.4.
[51] T., Damour, M., Henneaux and H., Nicolai, “Cosmological billiards,” Class. Quant. Grav. 20, R145 (2003) [arXiv:hep-th/0212256]. See Introduction, §3.3, 5.2, 5.5, 5.6, 5.8, 5.10.2, 6.4, 6.7, 7.7.
[52] T., Damour, M., Henneaux, A. D., Rendall and M., Weaver, “Kasner like behavior for subcritical Einstein matter systems,” Ann. Inst. Henri Poincaré 3, 1049 (2002) [gr-qc/0202069]. See Introduction, §3.2, 4.7, 6.5.4.
[53] T., Damour and C., Hillmann, “Fermionic Kac–Moody billiards and supergravity,” JHEP 0908, 100 (2009) [arXiv:0906.3116 [hep-th]]. See §C.3.
[54] T., Damour, A., Kleinschmidt and H., Nicolai, “Hidden symmetries and the fermionic sector of eleven-dimensional supergravity,” Phys. Lett. B 634, 319 (2006) [hep-th/0512163]. See §C.3.
[55] T., Damour, A., Kleinschmidt and H., Nicolai, “K(E(10)), supergravity and fermions,” JHEP 0608, 046 (2006) [hep-th/0606105]. See §C.3.
[56] T., Damour and P., Spindel, “Quantum supersymmetric cosmology and its hidden Kac–Moody structure,” Class. Quant. Grav. 30, 162001 (2013) [arXiv:1304.6381 [gr-qc]]. See §C.3.
[57] G., Dautcourt, “On the ultrarelativistic limit of general relativity,” Acta Phys. Polon. B 29, 1047 (1998) [arXiv:gr-qc/9801093]. See §6.7.
[58] S., de Buyl, M., Henneaux and L., Paulot, “Hidden symmetries and Dirac fermions,” Class. Quant. Grav. 22, 3595 (2005) [hep-th/0506009]. See §C.3.
[59] S., de Buyl, M., Henneaux and L., Paulot, “Extended E(8) invariance of 11-dimensional supergravity,” JHEP 0602, 056 (2006) [hep-th/0512292]. See §C.3.
[60] S., de Buyl and C., Schomblond, “Hyperbolic Kac–Moody algebras and Einstein billiards,” J. Math. Phys. 45, 4464 (2004) [hep-th/0403285]. See §D.8.
[61] J., Demaret, Y., De Rop and M., Henneaux, “Chaos in nondiagonal spatially homogeneous cosmological models in space-time dimensions ≤ 10,” Phys. Lett. B 211, 37 (1988). See §4.6.2.
[62] J., Demaret, J. L., Hanquin, M., Henneaux, P., Spindel and A., Taormina, “The fate of the mixmaster behavior in vacuum inhomogeneous Kaluza–Klein cosmological models,” Phys. Lett. B 175, 129 (1986). See Introduction, §3.2, 4.1, 4.6.2, 7.6.1.
[63] J., Demaret, M., Henneaux and P., Spindel, “Nonoscillatory behavior in vacuum Kaluza–Klein cosmologies,” Phys. Lett. B 164, 27 (1985). See Introduction, §3.2, 4.1, Preface to 4.6, 4.6.1, 4.6.2, 7.6.1.
[64] B. S., DeWitt, “Quantum theory of gravity. 1. The canonical theory,” Phys. Rev. 160, 1113 (1967). See §5.2.
[65] P. A. M., Dirac, “The theory of gravitation in Hamiltonian form,” Proc. Roy. Soc. Lond. A 246, 333 (1958). See §5.1.
[66] D., Eardley, E., Liang and R., Sachs, “Velocity-dominated singularities in irrotational dust cosmologies,” J. Math. Phys. 13, 99 (1972). See Introduction, §4.7.
[67] C., Eckart, “The thermodynamics of irreversible processes III. Relativistic theory of the simple fluid,” Phys. Rev. 58, 919 (1940). See §4.8.1.
[68] L. P., Eisenhart, Riemannian Geometry, Princeton University Press, NJ, 1926. See §A.2.
[69] J., Ehlers, Dissertation Hamburg University (1957). See §7.7.
[70] Y., Elskens and M., Henneaux, “Chaos in Kaluza–Klein models,” Class. Quant. Grav. 4, L161 (1987). See §4.6.2.
[71] Y., Elskens and M., Henneaux, “Ergodic theory of the mixmaster model in higher space-time dimensions,” Nucl. Phys. B 290, 111 (1987). See §4.6.2.
[72] A., Eskin and C., McMullen, “Mixing, counting and equidistribution in Lie groups,” Duke Math. J. 71, 181–209 (1993). See §3.2, 5.9, 6.6.
[73] V. A., Fock and D., Ivanenko, “Géométrie quantique linéaire et déplacement parallèle,” Compt. Rend. Acad. Sci. Paris 188, 1470 (1929). See §C.1.
[74] E. S., Fradkin and M. A., Vasiliev, “On the gravitational interaction of massless higher spin fields,” Phys. Lett. B 189, 89 (1987). See §6.1.
[75] J., Fuchs, Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 1995. See §D.9.
[76] D., Garfinkle, “Numerical simulations of generic singuarities,” Phys. Rev. Lett. 93, 161101 (2004) [gr-qc/0312117]. See §4.7.
[77] D., Garfinkle, “Numerical relativity beyond astrophysics,” Rept. Prog. Phys. 80, no. 1, 016901 (2017) [arXiv:1606.02999 [gr-qc]]. See §4.7.
[78] R. P., Geroch, “A method for generating solutions of Einstein's equations,” J. Math. Phys. 12, 918 (1971). See §7.7.
[79] R. P., Geroch, “A method for generating new solutions of Einstein's equation. 2,” J. Math. Phys. 13, 394 (1972). See §7.7.
[80] G., Gibbons, K., Hashimoto and P., Yi, “Tachyon condensates, Carrollian contraction of Lorentz group, and fundamental strings,” JHEP 0209, 061 (2002) [arXiv:hep-th/0209034]. See §6.7.
[81] S. W., Goode, A. A., Coley and J., Wainwright “The isotropic singularity in cosmology,” Class. Quant. Grav. 9, 445 (1992). See Preface to 4.8, §4.8.2.
[82] A. J. S., Hamilton, “Inflation followed by BKL collapse inside accreting, rotating black holes,” arXiv:1703.01921 [gr-qc]. See §4.7.
[83] J. M., Heinzle and C., Uggla, “Mixmaster: fact and belief,” Class. Quant. Grav. 26, 075016 (2009) [arXiv:0901.0776 [gr-qc]]. See §2.5.
[84] S., Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Graduate Studies in Mathematics vol. 34, American Mathematical Society, Providence 2001. See §5.2.
[85] M., Henneaux, “Geometry of zero signature space-times,” Print-79-0606 (Princeton), published in Bull. Soc. Math. Belg. 31, 47 (1979) (note the misprints in the published version, absent in the preprint version). See §6.7.
[86] M., Henneaux, “Bianchi type I cosmologies and spinor fields,” Phys. Rev. D 21, 857 (1980). See §C.3.
[87] M., Henneaux, “Bianchi universes and spinor fields” (in French), Ann. Inst. H. Poincare Phys. Theor. 34, 329 (1981). See §C.3.
[88] M., Henneaux and B., Julia, “Hyperbolic billiards of pure D = 4 supergravities,” JHEP 0305, 047 (2003) [hep-th/0304233]. See §7.6.3, D.7, D.9.
[89] M., Henneaux, A., Kleinschmidt and H., Nicolai, “Real forms of extended Kac– Moody symmetries and higher spin gauge theories,” Gen. Rel. Grav. 44, 1787 (2012) [arXiv:1110.4460 [hep-th]]. See §D.9.
[90] M., Henneaux, D., Persson and P., Spindel, “Spacelike singularities and hidden symmetries of gravity,” Living Rev. Rel. 11, 1 (2008) [arXiv:0710.1818 [hep-th]]. See §7.3, 7.4, 7.5.3.
[91] M., Henneaux, M., Pilati and C., Teitelboim, “Explicit solution for the zero signature (strong coupling) limit of the propagation amplitude in quantum gravity,” Phys. Lett. B 110, 123 (1982). See §5.2.
[92] D., Hobill, A., Burd and A., Coley, (eds) Deterministic Chaos in General Relativity, NATO ASI Series B, Physics Vol. 332, Plenum Press, New York 1994. See §3.2.
[93] E., Hopf, “Statistik der geodätishen Linien in Mannigfaltigkeiten negativer Krümmung,” Berlin Verh. Sächs. Akad. Wiss. Leipzig 91, 261 (1939). See §3.2, 5.9, 6.6.
[94] R. E., Howe and C. C., Moore, “Asymptotic properties of unitary representations,” J. Functional Analysis 32, 72–96 (1979). See §3.2, 5.9, 6.6.
[95] J. E., Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics 29, Cambridge University Press, 1990. See §7.3, 7.4, 7.5.3, 7.5.4, D.8.
[96] G., Imponente and G., Montani, “On the Covariance of the Mixmaster Chaoticity,” Phys. Rev. D 63, 103501 (2001) [arXiv:astro-ph/0102067]. See §3.2.
[97] C. J., Isham, “Some quantum field theory aspects of the superspace quantization of general relativity,” Proc. Roy. Soc. Lond. A 351, 209 (1976). See §6.7.
[98] W., Israel, “Nonstationary irreversible thermodynamics: a causal relativistic theory,” Ann. Phys. 100, 310 (1976). See §4.8.1, 4.8.2.
[99] W., Israel and J. M., Stewart, “Transient relativistic thermodynamics and kinetic theory,” Ann. Phys. 118, 341 (1979). See §4.8.1.
[100] V. D., Ivashchuk, A. A., Kirillov and V. N., Melnikov, “Stochastic properties of multidimensional cosmological models near a singular point,” JETP Lett. 60, 235 (1994) [Pisma Zh. Eksp. Teor. Fiz. 60, 225 (1994)]. See §6.7.
[101] V. D., Ivashchuk and V. N., Melnikov, “Billiard representation for multidimensional cosmology with multicomponent perfect fluid near the singularity,” Class. Quant. Grav. 12, 809 (1995) [gr-qc/9407028]. See §6.7.
[102] V. D., Ivashchuk and V. N., Melnikov, “Billiard representation for multidimensional cosmology with intersecting p-branes near the singularity,” J. Math. Phys. 41, 6341 (2000) [arXiv:hep-th/9904077]. See §6.7.
[103] V. D., Ivashchuk and V. N., Melnikov, “Exact solutions in multidimensional gravity with antisymmetric forms,” Class. Quant. Grav. 18, R87 (2001) [hepth/ 0110274]. See §6.7.
[104] R. T., Jantzen, “The dynamical degrees of freedom in spatially homogeneous cosmology,” Commun. Math. Phys. 64, 211 (1979). See §B.4.
[105] R. T., Jantzen, “Spatially homogeneous dynamics: a unified picture,” arXiv:grqc/0102035. See §B.4.
[106] B., Julia, “Group disintegrations,” LPTENS 80/16, Invited paper presented at Nuffield Gravity Workshop, Cambridge, England, June 22–July 12, 1980. See §7.7.
[107] B., Julia, “Infinite dimensional groups acting on (super)gravity phase spaces,” in Proceedings of the Johns Hopkins Workshop on Current Problems in Particle Physics “Unified Theories and Beyond” (Johns Hopkins University, Baltimore, 1984). See §7.7.
[108] B., Julia, “On infinite dimensional symmetry groups in physics,” LPTENS-85/18, in Proceedings of the Symposium on the Occasion of the Niels Bohr Centennial: Recent Developments in Quantum Field Theory, edited by J., Ambjorn, B. J., Durhuus, J. L., Petersen, Amsterdam, North-Holland, 1985. See §7.7.
[109] B. L., Julia, “Dualities in the classical supergravity limits: dualizations, dualities and a detour via (4k+2)-dimensions,” in Cargese 1997, Strings, branes and dualities, pp. 121–139 [hep-th/9805083]. See §7.7.
[110] B., Julia and H., Nicolai, “Conformal internal symmetry of 2-d sigma models coupled to gravity and a dilaton,” Nucl. Phys. v 482, 431 (1996) [hep-th/9608082]. See §7.7.
[111] V. G., Kac, Infinite Dimensional Lie Algebra, 3rd edition, Cambridge University Press, 1990. See §5.10.2, 7.5.5, Preface to App.D, D.1, D.3, D.5, D.6.1, D.6.2, D.7, D.8, D.9.
[112] E., Kasner, “Geometrical theorems on Einstein's cosmological equations,” Am. J. Math. 43, 217 (1921). See §1.5.
[113] I. M., Khalatnikov, E. M., Lifshitz, K. M., Khanin, L. N., Shchur and Ya. G., Sinai, “On the stochasticity in relativistic cosmology,” Journ. Stat. Phys. 38, 97 (1985). See §3.1, 3.2.
[114] A., Ya. Khinchin, “Continued fractions,” University of Chicago Press, 1964; [Russian edition: Fizmatlit, Moscow, 1960]. See §3.1.
[115] A. A., Kirillov, “On the nature of the spatial distribution of metric inhomogeneities in the general solution of the Einstein equations near a cosmological singularity,” Sov. Phys. JETP 76, 355 (1993). See §6.7.
[116] A. A., Kirillov and A. A., Kochnev, “Cellular structure of space near a singularity in time in Einstein's equations,” JETP Letters 46, 436 (1987). See §3.3.
[117] A. A., Kirillov and V. N., Melnikov, “Dynamics of inhomogeneities of metric in the vicinity of a singularity in multidimensional cosmology,” Phys. Rev. D 52, 723 (1995) [gr-qc/9408004]. See §6.7.
[118] A. A., Kirillov and G. V., Serebryakov, “Origin of a classical space in quantum cosmologies,” Grav. Cosmol. 7, 211 (2001) [arXiv:hep-th/0012245]. See §6.7.
[119] R. O., Kuzmin, “Sur un problème de Gauss,” Atti del Congresso Internazionale dei Matematici, Bologna, Vol. 6, p. 83 (1928); [Russian publication: Doklady Akademii Nauk, serie A, p.375 (1928)]. See §3.1.
[120] L. D., Landau and E. M., Lifshitz, Classical Theory of Fields, Pergamon Press, Oxford, 1962. See §1.1, 1.4.
[121] L. D., Landau and E. M., Lifshitz, Fluid Mechanics, first English edition, Reading, Mass., 1958. [The first Russian edition appeared in 1944.] See §4.8.1, 4.8.2.
[122] E. M., Lifshitz, “On the gravitational stability of the expanding universe,” ZhETP 16, 587 (1946) (in Russian); reprinted: Journ. Phys. (USSR) 10, 116 (1946). See Preface to 4.8, §4.8.2.
[123] E. M., Lifshitz, I. M., Lifshitz and I. M., Khalatnikov, “Asymptotic analysis of oscillatory mode of approach to a singularity in homogeneous cosmological models,” Sov. Phys. JETP 32, 173, (1971) [Zh. Eksp. Teor. Fiz., 59, 322 (1970)]. See §3.1, 3.2, 4,3,1.
[124] E. M., Lifshitz and I. M., Khalatnikov, “Investigations in relativistic cosmology,” Adv. Phys. 12, 185 (1963). See §1.5, 1.6, 4.1, 4.8.2.
[125] W. C., Lim, L., Andersson, D., Garfinkle and F., Pretorius, “Spikes in the mixmaster regime of G(2) cosmologies,” Phys. Rev. D 79, 123526 (2009) [arXiv:0904.1546 [gr-qc]]. See §1.4.
[126] U., Lindström and H. G., Svendsen, “A pedestrian approach to high energy limits of branes and other gravitational systems,” Int. J. Mod. Phys. A 16, 1347 (2001) [arXiv:hep-th/0007101]. See §6.7.
[127] V. N., Lukash, “Homogeneous cosmological models with gravitational waves and rotation,” Pis'ma Zh. Eksp. Teor. Fiz. 19, 449 (1974). See §4.2.
[128] V. N., Lukash, “Physical interpretation of homogeneous cosmological models,” Nuovo Cimento 35, 268 (1976). See §4.2.
[129] G. A., Margulis, “Applications of ergodic theory to the investigation of manifolds of negative curvature,” Funct. Anal. Appl. 4, 335 (1969). See §3.2, 5.9, 6.6.
[130] C. W., Misner, “Mixmaster universe,” Phys. Rev. Lett. 22, 1071–1074 (1969). See Introduction, §2.4.
[131] C. W., Misner, “Quantum cosmology. 1,” Phys. Rev. 186, 1319 (1969); also in “Minisuperspace,” in Magic Without Magic, pp. 441–473, J R Klauder ed., Freeman, San Francisco 1972. See §6.7.
[132] C. W., Misner, in: D., Hobill et al. (Eds), Deterministic Chaos in General Relativity, Plenum, 1994, pp. 317–328 [gr-qc/9405068]. See §6.7.
[133] C. W., Misner, K. S., Thorne, J. A., Wheeler, Gravitation, Freeman, 1973. See §5.1.
[134] G., Montani, “On the asymptotic regime of approach to a singular point in the general cosmological solution of the Einstein equations,” Tesi di Laurea, Università di Roma, Facolta di Fisica, 1992. See §3.3.
[135] R. V., Moody and A., Pianzola, Lie Algebras with Triangular Decomposition, Wiley, New York, 1995. See Preface to App. D.
[136] H., Nicolai, “A hyperbolic Lie algebra from supergravity,” Phys. Lett. B 276, 333 (1992). See §7.7.
[137] H., Nicolai, in Recent Aspects of Quantum Fields, Proceedings Schladming 1991, Lecture Notes in Physics, Springer Verlag, 1991. See §7.7.
[138] R., Penrose, “Gravitational collapse and space-time singularities,” Phys. Rev. Lett. 14, 57 (1965). See §1.10.
[139] R., Penrose, “Singularities and time-asymmetry,” in General Relativity: An Einstein Centenary Survey, p. 581, Cambridge University Press (1979). See Preface to 4.8.
[140] A. A., Peresetskii, “Singularity of homogeneous Einstein metrics,” Mat. Zametki 21, 71 (1977). See §4.2.
[141] W., Piechocki and G., Plewa, “Structures arising in the asymptotic dynamics of the Bianchi IX model,” arXiv:1611.05262 [gr-qc]. See §2.4.
[142] J., Polchinski, String Theory, two volumes, Cambridge University Press, Cambridge, 1998. See §6.1, 7.6.3.
[143] J. G., Ratcliffe, Foundations of Hyperbolic Manifolds, Graduate Texts in Mathematics 149, 2nd edition, Springer, 2006. See §7.3, 7.4.
[144] H., Ringström, “The Bianchi IX attractor,” Ann. Inst. Henri Poincaré 2, 405–500 (2001). See §4.7.
[145] S. E., Rugh, “Chaos in the Einstein equations – characterisation and importance?” in Deterministic Chaos in General Relativity, pp. 359–422, edited by D., Hobill et al., Plenum Press, 1994. See §3.2.
[146] C., Saçlioğlu, “Dynkin diagrams for hyperbolic Kac–Moody algebras,” J. Phys A: Math. Gen. 22, 3753 (1989). See §5.10.2, D.8.
[147] J. M. M., Senovilla, “Singularity theorems and their consequences,” Gen. Rel. Grav. 30, 701 (1998). See §1.10.
[148] J. M. M., Senovilla, “Singularity theorems in general relativity: achievements and open questions,” Einstein Stud. 12, 305 (2012) [physics/0605007]. See §1.10.
[149] Ya. G., Sinai, “The stochasticity of dynamical systems,” Selecta Math. Soviet., 1(1), pp. 100–119 (1981). See §3.2, 5.9, 6.6.
[150] Ya. G., Sinai, “Geodesic flows on manifolds of negative curvature,” in Algoritms, Fractals and Dynamics pp. 201–215 (Okayama/Kyoto, 1992). Plenum, New York, 1995. See §3.2, 5.9, 6.6.
[151] C., Teitelboim, “The Hamiltonian structure of space-time,” PRINT-78-0682 (Princeton), in General Relativity and Gravitation, vol. 1, A. Held ed., Plenum Press, 1980. See §6.7.
[152] C., Uggla, “Recent developments concerning generic spacelike singularities,” Gen. Rel. Grav. 45, 1669 (2013) [arXiv:1304.6905 [gr-qc]]. See §2.5.
[153] C., Uggla, H., van Elst, J., Wainwright and G. F. R., Ellis, “The past attractor in inhomogeneous cosmology,” Phys. Rev. D 68, 103502 (2003) [gr-qc/0304002]. See §2.5.
[154] E. B., Vinberg, O. B., Shvartsman, “Discrete groups of motions of spaces of constant curvature,” Encyclopaedia of Mathematical Sciences, vol. 29, Springer, 1991. See §7.3, 7.4, 7.5.1, 7.5.2.
[155] P. C., West, “E11 and M theory,” Class. Quant. Grav. 18, 4443–4460 (2001), [arXiv:hep-th/0104081]. See §7.7.
[156] A., Zardecki, “Modelling in chaotic relativity,” Phys. Rev. D 28, 1235 (1983). See §3.2.
[157] Ya. B., Zeldovich, “The equation of state at ultrahigh densities and its relativistic limitation,” Sov. Phys. JETP 14, 1143 (1962) [Zh. Eksp. Teor. Fiz. 41, 1609 (1961)]. See §4.1.
[158] R., Zimmer, Ergodic Theory and Semisimple Groups, Birkhauser, Boston, 1984. See §3.2, 5.9, 6.6.
