Homotopical Dynamics IV: Hopf invariants and hamiltonian flows

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Cornea, Octavian (2001)
  • Subject: 55Q25 | Mathematics - Algebraic Topology | Mathematics - Dynamical Systems | 57R70 | 37J45

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 $C^{1}$-closing lemma leads to periodic ones.
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