TY - JOUR

T1 - Chaotic diffusion on periodic orbits

T2 - The perturbed Arnold cat map

AU - Dana, Itzhack

AU - Chernov, Vladislav E.

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85037213744&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.67.046203

DO - 10.1103/PhysRevE.67.046203

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AN - SCOPUS:85037213744

SN - 1063-651X

VL - 67

SP - 7

JO - Physical Review E

JF - Physical Review E

IS - 4

ER -