Chaotic Diffusion on Periodic Orbits: The Perturbed Arnol'd Cat Map

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dc.creatorDana, Itzhack
dc.creatorChernov, Vladislav E.
dc.date2003-03-09
dc.date.accessioned2026-07-07T06:36:13Z
dc.date.available2026-07-07T06:36:13Z
dc.descriptionChaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnol'd 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: (a) The curvature expansion of the Ruelle zeta function. (b) The average of the PO winding-number squared, $w^{2}$, weighted by a stability factor. (c) The uniform (nonweighted) average of $w^{2}$. The results from formulas (a) and (b) agree very well with those obtained by standard methods, for all the perturbation parameters considered. Formula (c) gives reasonably accurate results for sufficiently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to {\em uniformity sum rules} satisfied by the PO Lyapunov eigenvalues at {\em fixed} $w$. These sum rules follow from general arguments and are supported by much numerical evidence.
dc.description6 Tables, 2 Figures (postscript); To appear in Physical Review E
dc.identifierhttps://arxiv.org/abs/nlin/0303018
dc.identifierhttp://arxiv.org/abs/nlin/0303018
dc.identifierPhysical Review E vol. 67, 046203 (2003)
dc.identifierdoi:10.1103/PhysRevE.67.046203
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100013
dc.subjectChaotic Dynamics
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subjectPlasma Physics
dc.titleChaotic Diffusion on Periodic Orbits: The Perturbed Arnol'd Cat Map
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