Chaotic diffusion on periodic orbits: The perturbed Arnold cat map

Itzhack Dana, Vladislav E. Chernov

Research output: Contribution to journalArticlepeer-review

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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 [Formula presented] function; (2) the average of the PO winding-number squared, [Formula presented] weighted by a stability factor; (3) the uniform (nonweighted) average of [Formula presented] 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.

Original languageEnglish
Pages (from-to)7
Number of pages1
JournalPhysical Review E
Issue number4
StatePublished - 2003


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