Rotation Vectors and Fixed Points of Area Preserving Surface Diffeomorphisms
نویسندگان
چکیده
منابع مشابه
Homoclinic Points for Area-preserving Surface Diffeomorphisms
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 Hami...
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We prove some generic properties for Cr , r = 1, 2, . . . ,∞, areapreserving diffeomorphism on compact surfaces. The main result is that the union of the stable (or unstable) manifolds of hyperbolic periodic points are dense in the surface. This extends the result of Franks and Le Calvez [8] on S to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.
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Let M be a compact n-dimensional manifold and ω be a symplectic or volume form on M. Let φ be a C1 diffeomorphism on M that preserves ω and let p be a hyperbolic periodic point of φ. We show that generically p has a homoclinic point, and moreover, the homoclinic points of p is dense on both stable manifold and unstable manifold of p. Takens [11] obtained the same
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1996
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-96-01502-4