Homoclinic Points for Area-preserving Surface Diffeomorphisms
نویسنده
چکیده
We show a Cr connecting lemma for area-preserving surface diffeomorphisms and for periodic Hamiltonian on surfaces. We prove that for a generic Cr , r = 1, 2, . . ., ∞, 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 Cr, r = 1, 2, . . ., ∞ 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.
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تاریخ انتشار 2006