Abstract
We study a class of twist maps where the functiong(θ)=θ(1−|2θ|z−1) is nonanalytic (C 1) and endowed with a varying degree of inflectionz. Whenz>3, reappearance of a KAM torus after its breakup has been observed. We introduce an “inverse residue criterion” to determine the reappearance point. Scaling behavior at the transition points is also studied. For 2⩽z<3 the scaling exponents are found to vary withz, whereas forz⩾3 they are independent ofz. In this sensez=3 plays a role quite similar to that of the upper critical dimension in phase transitions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. M. Greene,J. Math. Phys. 20:1183 (1979).
L. P. Kadanoff,Phys. Rev. Lett. 47:1641 (1981); S. J. Shenker and L. P. Kadanoff,J. Stat. Phys. 27:631 (1982).
R. S. MacKay,Physica D 7:283 (1983).
B. Hu and J. M. Mao,Phys. Rev. A 25:3259 (1982); B. Hu and I. Satija,Phys. Lett. A 98:143 (1983).
S. Ostlund, D. Rand, J. Sethna, and E. Siggia,Physica D 8:303 (1983).
B. Hu, A. Valinia, and O. Piro,Phys. Lett. A 144:7 (1990).
H. J. Schellnhuber and H. Urbschat,Phys. Rev. Lett. 54:588 (1985).
J. Wilbrink,Physica D 26:385 (1987).
J. A. Ketoja and R. S. MacKay,Physica D 35:318 (1989).
J. N. Mather,Math. Publ. IHES 63:163 (1982);Erg. Th. Dyn. Sys. 4:301 (1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hu, B., Shi, J. & Kim, S.Y. Recurrence of Kolmogorov-Arnold-Moser tori in nonanalytic twist maps. J Stat Phys 62, 631–649 (1991). https://doi.org/10.1007/BF01017977
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01017977