Closed trajectories on symmetric convex Hamiltonian energy surfaces

Wei Wang

doi:10.3934/dcds.2012.32.679

Article Contents

2012, Volume 32, Issue 2: 679-701. Doi: 10.3934/dcds.2012.32.679

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Closed trajectories on symmetric convex Hamiltonian energy surfaces

Wei Wang^1,

1.
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Science, Peking University, Beijing, 100871

Received: August 2010

Revised: May 2011

Published: February 2012

Abstract / Introduction Related Papers Cited by

Abstract

In this article, let $\Sigma\subset\mathbf{R}^{2n}$ be a compact convex Hamiltonian energy surface which is symmetric with respect to the origin, where $n\ge 2$. We prove that there exist at least two geometrically distinct symmetric closed trajectories of the Reeb vector field on $\Sigma$.

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Mathematics Subject Classification: Primary: 58E05, 37J45; Secondary: 37C75.

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