English

Integrable Approximation of Regular Islands: The Iterative Canonical Transformation Method

Chaotic Dynamics 2013-12-06 v2 Exactly Solvable and Integrable Systems

Abstract

Generic Hamiltonian systems have a mixed phase space, where classically disjoint regions of regular and chaotic motion coexist. We present an iterative method to construct an integrable approximation, which resembles the regular dynamics of a given mixed system and extends it into the chaotic region. The method is based on the construction of an integrable approximation in action representation which is then improved in phase space by iterative applications of canonical transformations. This method works for strongly perturbed systems and arbitrary degrees of freedom. We apply it to the standard map and the cosine billiard.

Keywords

Cite

@article{arxiv.1308.1561,
  title  = {Integrable Approximation of Regular Islands: The Iterative Canonical Transformation Method},
  author = {Clemens Löbner and Steffen Löck and Arnd Bäcker and Roland Ketzmerick},
  journal= {arXiv preprint arXiv:1308.1561},
  year   = {2013}
}

Comments

13 pages, 12 figures

R2 v1 2026-06-22T01:05:24.324Z