# American Institute of Mathematical Sciences

January  2000, 6(1): 243-253. doi: 10.3934/dcds.2000.6.243

## Homoclinic points and intersections of Lagrangian submanifold

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

Received  November 1999 Published  December 1999

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.
Citation: Zhihong Xia. Homoclinic points and intersections of Lagrangian submanifold. Discrete & Continuous Dynamical Systems, 2000, 6 (1) : 243-253. doi: 10.3934/dcds.2000.6.243
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