PMID: 12786456Jun 6, 2003Paper

Chaotic diffusion on periodic orbits: the perturbed Arnold cat map

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Itzhack Dana, Vladislav E Chernov

Abstract

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnold cat map on a cylinder, in a range of perturbation parameters corresponding to an extended structural-stability regime of the system on the torus. The diffusion coefficient is calculated, using the following PO formulas: (1). the curvature expansion of the Ruelle zeta function; (2). the average of the PO winding-number squared, w(2), weighted by a stability factor; (3). the uniform (nonweighted) average of w(2). The results from formulas (1). and (2). agree very well with those obtained by standard methods, for all the perturbation parameters considered. Formula (3). gives reasonably accurate results for sufficiently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to uniformity sum rules satisfied by the PO Lyapunov eigenvalues at fixed w. These sum rules follow from general arguments and are supported by much numerical evidence.

References

Apr 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·I Dana, M Amit
Mar 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·I Dana, T Kalisky
Jan 16, 1989·Physical Review Letters·I DanaI C Percival
May 14, 1990·Physical Review Letters·I Dana
Jan 1, 1992·Chaos·Predrag CvitanovicThomas Schreiber

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Citations

Dec 1, 2004·Chaos·Ljupco KocarevGabor Vattay
Feb 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·O Barash, I Dana
Apr 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tomaž Prosen

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