### 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 language | English |
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Pages (from-to) | 783-793 |

Number of pages | 11 |

Journal | Progress of Theoretical Physics |

Volume | 98 |

Issue number | 4 |

Publication status | Published - 1997 Oct |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical Physics*,

*98*(4), 783-793.

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

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 98, no. 4, pp. 783-793.

}

TY - JOUR

T1 - Breakup process and geometrical structure of high-dimensional KAM tori

AU - Kurosaki, Satoru

AU - Aizawa, Yoji

PY - 1997/10

Y1 - 1997/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0031318666&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031318666&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031318666

VL - 98

SP - 783

EP - 793

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 4

ER -