Homoclinic points and intersections of Lagrangian submanifold

Zhihong Xia

doi:10.3934/dcds.2000.6.243

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2000, Volume 6, Issue 1: 243-253. Doi: 10.3934/dcds.2000.6.243

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Homoclinic points and intersections of Lagrangian submanifold

Zhihong Xia^1,

1.
Department of Mathematics, Northwestern University, Evanston, Illinois 60208

Received: October 31, 1999

Published: December 1999

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Abstract

In this paper, we prove certain persistence properties of the homoclinic points in Hamiltonian systems and symplectic diffeomorphisms. We show that, under some general conditions, stable and unstable manifolds of hyperbolic periodic points intersect in a very persistent way and we also give some simple criteria for positive topological entropy. The method used is the intersection theory of Lagrangian submanifolds of symplectic manifolds.

Keywords:

Homoclinic points,
Lagrangian submanifold.

Mathematics Subject Classification: 37G25.

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