### Abstract

The classical dynamical system can have the negative curvature region where orbital instability takes place. But it is not yet clear whether this system has instability in the large. To see this a dynamical system with the hamiltonian (equation) is studied by the method of the surface of section. The system does not have negative curvature for ε ^{z.ast;}≤0 but can have negative curvature locally for ε ^{z.ast;}≥0. For the case of ε ^{z.ast;}≤0 isolating integrals exist globally, but for the case of ε ^{z.ast;}≥0 the instability zone extends to larger region beyond that of negative curvature.

Original language | English |
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Pages (from-to) | 1693-1696 |

Number of pages | 4 |

Journal | Journal of the Physical Society of Japan |

Volume | 33 |

Issue number | 6 |

Publication status | Published - 1972 Dec |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*33*(6), 1693-1696.

**Instability of a classical dynamical system with the negative curvature region.** / Aizawa, Yôji.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 33, no. 6, pp. 1693-1696.

}

TY - JOUR

T1 - Instability of a classical dynamical system with the negative curvature region

AU - Aizawa, Yôji

PY - 1972/12

Y1 - 1972/12

N2 - The classical dynamical system can have the negative curvature region where orbital instability takes place. But it is not yet clear whether this system has instability in the large. To see this a dynamical system with the hamiltonian (equation) is studied by the method of the surface of section. The system does not have negative curvature for ε z.ast;≤0 but can have negative curvature locally for ε z.ast;≥0. For the case of ε z.ast;≤0 isolating integrals exist globally, but for the case of ε z.ast;≥0 the instability zone extends to larger region beyond that of negative curvature.

AB - The classical dynamical system can have the negative curvature region where orbital instability takes place. But it is not yet clear whether this system has instability in the large. To see this a dynamical system with the hamiltonian (equation) is studied by the method of the surface of section. The system does not have negative curvature for ε z.ast;≤0 but can have negative curvature locally for ε z.ast;≥0. For the case of ε z.ast;≤0 isolating integrals exist globally, but for the case of ε z.ast;≥0 the instability zone extends to larger region beyond that of negative curvature.

UR - http://www.scopus.com/inward/record.url?scp=0001966905&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001966905&partnerID=8YFLogxK

M3 - Article

VL - 33

SP - 1693

EP - 1696

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 6

ER -