Homoclinic Points For Area-Preserving Surface Diffeomorphisms

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dc.creatorXia, Zhihong
dc.date2006-06-13
dc.date.accessioned2026-07-07T07:17:13Z
dc.date.available2026-07-07T07:17:13Z
dc.descriptionWe show a $C^r$ connecting lemma for area-preserving surface diffeomorphisms and for periodic Hamiltonian on surfaces. We prove that for a generic $C^r$, $r=1, 2, ...$, $\infty$, area-preserving diffeomorphism on a compact orientable surface, homotopic to identity, every hyperbolic periodic point has a transversal homoclinic point. We also show that for a $C^r$, $r=1, 2, ...$, $\infty$ generic time periodic Hamiltonian vector field in a compact orientable surface, every hyperbolic periodic trajectory has a transversal homoclinic point. The proof explores the special properties of diffeomorphisms that are generated by Hamiltonian flows.
dc.identifierhttps://arxiv.org/abs/math/0606291
dc.identifierhttp://arxiv.org/abs/math/0606291
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113863
dc.subjectDynamical Systems
dc.subject37E30; 37J10
dc.titleHomoclinic Points For Area-Preserving Surface Diffeomorphisms
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