The Conley-Zehnder index and the saddle-center equilibrium

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:220

Article

Grotta-Ragazzo, C ; Salomao, PAS

关键词: Hamiltonian systems;    Conley-Zehnder index;    convexity;    saddle-center;    two-degrees of freedom;   

DOI  :  10.1016/j.jde.2005.03.015

来源: Elsevier

【 摘 要 】

We consider Hamiltonian systems with two degrees of freedom. We suppose the existence of a saddle-center equilibrium in a strictly convex component S of its energy level. Moser's normal form for such equilibriums and a theorem of Hofer, Wysocki and Zehnder are used to establish the existence of a periodic orbit in S with several topological properties. We also prove the explosion of the Conley-Zehnder index of any periodic orbit that passes close to the saddle-center equilibrium. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free