Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Rashevskii P.K. On connection of any two points by the admissible curve.-Zapiski Mosc.Inst.K.Libknexta. Ser.phys.-math.,1938,N 2, p.83–94 (in Russian).
Vershik A.M., Gershkovich V.Ya. Nonholonomic problem and distribution geometry.-The addition to Russian translation of [6].
Dubrovin B.A., Novikov S.P.,Fomenko A.T. The modern geometry. M.: Nauka,1979 (in Russian).
Auslander L.,Green L.,Hahn F. Flows on homogeneous Spaces. Princeton Univ.Press,1963.
Arnol'd V.I., Varchenko A.M.,Gusein-Zade S.M. The smooth map singularities. v.I,2. M.: Nauka,1982,1984 (in Russian).
Griffits Ph.A. Exterior differential system and calculus of Variations. Boston: Birkhauser,1983.
Bourbaki N. Groups et algebres de Lie. Ch.I-3. Hermann, Paris, 1971,1972.
Lefshetz S. Differential equations. Geometric theory. N.Y.: Interscience publ.,1957.
Vershik A.M.,Gershkovich V.Ya. Nonholonomic geodesic flow on SL2ℝ.-Zapiski Sem.LOMI AN USSR, v.155,1986 (in Russian).
Pansu P. Croissance des boules et des geodesiques fermees dans les nilvarietes.-Ergodic theory and dynamic system 1983,3,p.3, 415–446.
Mitchel J. On Carno-Caratheodori metrics.-Jour.of diff.geom., 1985,21,No I,p.35–42.
Gromov M. Groups of polynomial growth and expanding maps.-Inst. Haytes Sci.Publ.Math., No 53, 1981.
Kaimanovich V.A.,Vershik A.M. Random walks on discrete groups: Boundary and entropy.-The annals of probability,1983,v.II,No 3, p.457–490.
Lobry C. Dynamical polysystems and control theory. Geometric methods in system theory.-Proceedings of Nato Adv.Inst.Boston: Reidell Publ.Comp.,1973,p.1–42.
Sussmann H.J. Orbits families of vector fields and integrabilities of distributions.-Trans.Amer.Math.Soc.,1973,180,171–188.
Rund H. The differential geometry of Finsper spaces. Berlin,1959.
Gershkovich V.Ya. Two-sided estimates of metric generated by absolutely nonholonomic distributions.-Soviet Math.Dokl.,v.30, 1984, No 2,p.506–510.
Vershik A.M., Gershkovich V.Ya. Nonholonomic dynamic system. Distribution on geometry and calculus of variations.-Modern problem in Math.Fundamental branches. Dymanic system-7. VINITI Acad. Sci.USSR,1987 (in Russian).
Nagel A.,Stein E.M.,Wainger S. Balls and metrics defined by vector fields I: Basic properties.-Acta Math.,155:1–2,p.103–148.
Filippov A.F. On some problems of control theory.-Vestnik MGU, ser.math.,1959, N 2,p.25–32 (in Russian).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this chapter
Cite this chapter
Vershik, A.M., Gershkovich, V. (1988). The geometry of the nonholonomic sphere for three-dimensional lie group. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A. (eds) Global Analysis — Studies and Applications III. Lecture Notes in Mathematics, vol 1334. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080435
Download citation
DOI: https://doi.org/10.1007/BFb0080435
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50019-3
Online ISBN: 978-3-540-45894-4
eBook Packages: Springer Book Archive