### 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 |

巻 | 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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### All Science Journal Classification (ASJC) codes

- Analysis

### これを引用

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

研究成果: ジャーナルへの寄稿 › 記事

}

TY - JOUR

T1 - N-homoclinic bifurcations for homoclinic orbits changing their twisting

AU - Nii, Shunsaku

PY - 1996/1/1

Y1 - 1996/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000933820&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000933820&partnerID=8YFLogxK

U2 - 10.1007/BF02218844

DO - 10.1007/BF02218844

M3 - Article

VL - 8

SP - 549

EP - 572

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

IS - 4

ER -