Breakup process and geometrical structure of high-dimensional KAM tori

Satoru Kurosaki, Yoji Aizawa

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The breakup of KAM tori in four-dimensional symplectic maps is studied. KAM tori are constructed explicitly by conjugation theory, and the successive steps leading to their breakup is analytically determined for two cases in which rotation vectors are cubic and quadratic. The present paper is motivated by the observation of Boltt and Meiss (Physica D66(1993), 282), but our result differs significantly from their conjecture, because it suggests that the rational approximation does not work in cases with many degrees of freedom. The succession to the breakup depends on the perturbations which determine the dominant type of small divisors in the conjugation function.

Original languageEnglish
Pages (from-to)783-793
Number of pages11
JournalProgress of Theoretical Physics
Volume98
Issue number4
Publication statusPublished - 1997 Oct

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conjugation
degrees of freedom
perturbation
approximation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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Breakup process and geometrical structure of high-dimensional KAM tori. / Kurosaki, Satoru; Aizawa, Yoji.

In: Progress of Theoretical Physics, Vol. 98, No. 4, 10.1997, p. 783-793.

Research output: Contribution to journalArticle

Kurosaki, Satoru ; Aizawa, Yoji. / Breakup process and geometrical structure of high-dimensional KAM tori. In: Progress of Theoretical Physics. 1997 ; Vol. 98, No. 4. pp. 783-793.
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