N-homoclinic bifurcations for homoclinic orbits changing their twisting

研究成果: ジャーナルへの寄稿記事

15 引用 (Scopus)

抄録

We study bifurcations, called N-homoclinic bifurcations, which produce homoclinic orbits rounding N times (N≥2) in some tubular neighborhood of original homoclinic orbit A family of vector fields undergoes such a bifurcation when it is a perturbation of a vector field with a homoclinic orbit. N-Homoclinic bifurcations are divided into two cases; one is that the linearization at the equilibrium has only real principal eigenvalues, and the other is that it has complex principal eigenvalues. We treat the former case, espcially that linearization has only one unstable eigenvalue. As main tools we use a topological method, namely, Conley index theory, which enables us to treat more degenerate cases than those studied by analytical methods.

元の言語英語
ページ(範囲)549-572
ページ数24
ジャーナルJournal of Dynamics and Differential Equations
8
発行部数4
DOI
出版物ステータス出版済み - 1 1 1996
外部発表Yes

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Homoclinic Bifurcation
Homoclinic Orbit
Principal Eigenvalue
Linearization
Vector Field
Bifurcation
Conley Index
Topological Methods
Index Theory
Rounding
Analytical Methods
Unstable
Eigenvalue
Perturbation

All Science Journal Classification (ASJC) codes

  • Analysis

これを引用

N-homoclinic bifurcations for homoclinic orbits changing their twisting. / Nii, Shunsaku.

:: Journal of Dynamics and Differential Equations, 巻 8, 番号 4, 01.01.1996, p. 549-572.

研究成果: ジャーナルへの寄稿記事

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