Few islands approximation of Hamiltonian system with divided phase space
Bunimovich, Leonid A. (Author), Casati, Giulio (Author), Prosen, Tomaž (Author), Vidmar, Gregor (Author)

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It is well known that typical Hamiltonian systems have divided phase space consisting of regions with regular dynamics on KAM tori and region(s) with chaotic dynamics called chaotic sea(s). This complex structure makes rigorous analysis of such systems virtually impossible and significantly complicates numerical exploration of their dynamical properties. Hamiltonian systems with sharply divided phase space between regions of regular and chaotic dynamics are much easier to analyze, but there are only few cases or families of such systems known to date. In this article, we outline a new approach for a systematic construction, starting from a generic KAM Hamiltonian system, of a system with a sharply divided phase space with an arbitrary number of regular islands which are in one-to-one correspondence with islands of the initial KAM system. In this procedure a typical Hamiltonian system, for example a KAM billiard, is replaced by a sequence of Hamiltonian systems having an increasing (but finite) number of islands of regular motion. The islands in the substituting systems are sub-islands of the KAM islands in the initial system. We apply this idea to two-dimensional lemon-shaped billiards, where the substituting systems are obtained by replacing parts of the curved boundaries by chords, so that in the limit of infinite number of islands the boundary of the substituting system becomes arbitrary close to the original billiard’s boundary.

Keywords:dynamical systems, Hamiltonian systems, chaos
Tipology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Number of pages:10 str.
ISSN on article:1058-6458
DOI:10.1080/10586458.2018.1559777 This link opens in a new window
COBISS.SI-ID:3300964 This link opens in a new window
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Record is a part of a journal

Title:Experimental mathematics
Shortened title:Exp. math.
Publisher:Jones and Bartlett Publishers
COBISS.SI-ID:2689113 This link opens in a new window

Document is financed by a project

Funder:EC - European Commission
Funding Programme:H2020
Project no.:694544
Name:Open many-body non-equilibrium systems

Secondary language

Keywords:dinamični sistemi, Hamiltonski sistemi, kaos

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