Periodic orbits of Hamiltonian flows near symplectic extrema

Viktor L. Ginzburg, Ely Kerman

Research output: Contribution to journalArticle

Abstract

For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bottnondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a nondegenerate (i.e., symplectic) magnetic field has periodic orbits on a sequence of energy levels converging to zero.

Original languageEnglish (US)
Pages (from-to)69-91
Number of pages23
JournalPacific Journal of Mathematics
Volume206
Issue number1
DOIs
StatePublished - Sep 2002
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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