Abstract
Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnol'd cat map, exhibiting a transition from uniform to nonuniform hyperbolicity as the perturbation parameter is increased. The results for the diffusion coefficient from PO formulas agree very well with those obtained by standard methods. Using the original PO formula involving a uniform (nonweighted) average over the POs, reasonably accurate results are obtained 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 winding number.
| Original language | English |
|---|---|
| Pages (from-to) | 253-258 |
| Number of pages | 6 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 330 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - 1 Dec 2003 |
| Event | Randomes and Complexity - Eilat, Israel Duration: 5 Jan 2003 → 9 Jan 2003 |
Bibliographical note
Funding Information:We thank J.M. Robbins for discussions. This work was partially supported by the Israel Science Foundation administered by the Israel Academy of Sciences and Humanities. V.E.C. acknowledges the CRDF and Ministry of Education of the Russian Federation for Award #VZ-010-0.
Funding
We thank J.M. Robbins for discussions. This work was partially supported by the Israel Science Foundation administered by the Israel Academy of Sciences and Humanities. V.E.C. acknowledges the CRDF and Ministry of Education of the Russian Federation for Award #VZ-010-0.
| Funders | Funder number |
|---|---|
| Citrus Research and Development Foundation | |
| Ministry of Education and Science of the Russian Federation | -010-0 |
| Israel Academy of Sciences and Humanities | |
| Israel Science Foundation |
Keywords
- Arnol'd cat map
- Chaotic diffusion
- Hyperbolic Hamiltonian systems
- Periodic orbits
- Structural stability