## Abstract

By generalizing the Floquet method from periodic systems to systems with exponential dichotomy, a local coordinate system is established in a neighborhood of the heteroclinic loop Γ to study the bifurcation problems of homo-clinic and periodic orbits. Asymptotic expressions of the bifurcation surfaces and their relative positions are given. The results obtained in literature concerned with the 1-hom bifurcation surfaces are unproved and extended to the nontransversal case. Existence regions of the 1-per orbits bifurcated from Γ are described, and the uniqueness and incoexistence of the 1-hom and 1-per orbit and the inexistence of the 2-hom and 2-per orbit are also obtained.

Original language | English (US) |
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Pages (from-to) | X6-848 |

Number of pages | 12 |

Journal | Science in China, Series A: Mathematics, Physics, Astronomy |

Volume | 41 |

Issue number | 8 |

DOIs | |

State | Published - Dec 1 1998 |

## Keywords

- Heteroclinic orbit
- Homoclinic bifurcation
- Periodic orbit bifurcation

## ASJC Scopus subject areas

- Mathematics(all)