BIFURCATIONS TO A HETEROCLINIC MANIFOLD WITH NONHYPERBOLIC EQUILIBRIA IN Rn

数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (3): 293-302.

BIFURCATIONS TO A HETEROCLINIC MANIFOLD WITH NONHYPERBOLIC EQUILIBRIA IN Rⁿ

孙建华¹, Robert E. Kooij²

1. Nanjing University, Department of Mathematics, Nanjing 210008, China;
2. Delft University of Technology, Faculty of Technical Mathfirnatics and Informatics. Mekelweg, 2623 CD Delft. The Netherlands

收稿日期:1996-04-15 出版日期:1998-09-25 发布日期:1998-09-25

BIFURCATIONS TO A HETEROCLINIC MANIFOLD WITH NONHYPERBOLIC EQUILIBRIA IN Rⁿ

Sun Jianhua¹, Robert E. Kooij²

1. Nanjing University, Department of Mathematics, Nanjing 210008, China;
2. Delft University of Technology, Faculty of Technical Mathfirnatics and Informatics. Mekelweg, 2623 CD Delft. The Netherlands

Received:1996-04-15 Online:1998-09-25 Published:1998-09-25

摘要/Abstract

摘要： The authors study bifurcations from a heteroclinic manifold connecting two non-hyperbolic equilibrium P₀ and P₁ for a n-dimensional dynamical system. They show that under some assumptions, each equilibrium P_i splits into two equilibria P_i and P_i(α), i=0, 1, and find the Melnikov vector conditions assuring the existence of a heteroclinic orbit from P₁ (α) to P₀ (α) along directions that are tangent to the strong unstable (resp.strong stable) manifold of P₁ (α) (resp.P₀(α)). The exponential trichotomy and the unified and geometrical method are used to prove their results.

关键词: nonhyperbolic equilibrium, heteroclinic manifold, exponential trichotomy

Abstract: The authors study bifurcations from a heteroclinic manifold connecting two non-hyperbolic equilibrium P₀ and P₁ for a n-dimensional dynamical system. They show that under some assumptions, each equilibrium P_i splits into two equilibria P_i and P_i(α), i=0, 1, and find the Melnikov vector conditions assuring the existence of a heteroclinic orbit from P₁ (α) to P₀ (α) along directions that are tangent to the strong unstable (resp.strong stable) manifold of P₁ (α) (resp.P₀(α)). The exponential trichotomy and the unified and geometrical method are used to prove their results.

Key words: nonhyperbolic equilibrium, heteroclinic manifold, exponential trichotomy

孙建华, Robert E. Kooij. BIFURCATIONS TO A HETEROCLINIC MANIFOLD WITH NONHYPERBOLIC EQUILIBRIA IN Rⁿ[J]. 数学物理学报(英文版), 1998, 18(3): 293-302.

Sun Jianhua, Robert E. Kooij. BIFURCATIONS TO A HETEROCLINIC MANIFOLD WITH NONHYPERBOLIC EQUILIBRIA IN Rⁿ[J]. Acta mathematica scientia,Series B, 1998, 18(3): 293-302.

BIFURCATIONS TO A HETEROCLINIC MANIFOLD WITH NONHYPERBOLIC EQUILIBRIA IN Rⁿ

BIFURCATIONS TO A HETEROCLINIC MANIFOLD WITH NONHYPERBOLIC EQUILIBRIA IN Rⁿ

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