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Homotopical dynamics IV. Hopf invariants and Hamiltonian flows
Author(s) -
Cornea Octavian
Publication year - 2002
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3023
Subject(s) - mathematics , lagrangian , combinatorics , algebra over a field , mathematical physics , pure mathematics
In a non-compact context the first natural step in the search for periodicorbits of a hamiltonian flow is to detect bounded ones. In this paper we showthat, in a non-compact setting, certain algebraic topological constraintsimposed to a gradient flow of the hamiltonian function $f$ imply the existenceof bounded orbits for the hamiltonian flow of $f$. Once the existence ofbounded orbits is established, under favorable circumstances, application ofthe $C^{1}$-closing lemma leads to periodic ones.