The Conley-Zehnder index and the saddle-center equilibrium |
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Authors: | Clodoaldo Grotta-Ragazzo |
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Institution: | Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090 São Paulo, SP, Brazil |
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Abstract: | 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. |
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Keywords: | Hamiltonian systems Conley-Zehnder index Convexity Saddle-center Two-degrees of freedom |
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