Homoclinic points in symplectic and volume-preserving diffeomorphisms |
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Authors: | Zhihong Xia |
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Institution: | 1. Department of Mathematics, Northwetern University, 60208, Evanston, Illinois, USA
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Abstract: | LetM n be a compactn-dimensional manifold and ω be a symplectic or volume form onM n. Let ? be aC 1 diffeomorphism onM n that preserves ω and letp be a hyperbolic periodic point of Φ. We show that genericallyp has a homoclinic point, and moreover, the homoclinic points ofp is dense on both stable manifold and unstable manifold ofp. Takens 11] obtained the same result forn=2. |
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