Homotopical Dynamics IV: Hopf invariants and hamiltonian flows

2001/11/22 by Octavian Cornea, Cornea, Octavian
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Mathematical Dynamics and Fractals #math.AT #math.DS #msc:37J45 #msc:55Q25 #msc:57R70

paper · pdf · doi:10.48550/arxiv.math/0111247

54 pages

arxiv created 2001/11/22 · arxiv updated 2009/11/30

Abstract

In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a gradient flow of the hamiltonian function f imply the existence of bounded orbits for the hamiltonian flow of f. Once the existence of bounded orbits is established, under favorable circumstances, application of the C¹-closing lemma leads to periodic ones.

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