Area-preserving surface diffeomorphisms

Zhihong Xia

doi:10.1007/s00220-005-1514-3

Area-preserving surface diffeomorphisms

Zhihong Xia^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We prove some generic properties for C ^r , r = 1,2,. . .,∞, area-preserving 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 [10] on S ² to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.

Original language	English (US)
Pages (from-to)	723-735
Number of pages	13
Journal	Communications in Mathematical Physics
Volume	263
Issue number	3
DOIs	https://doi.org/10.1007/s00220-005-1514-3
State	Published - May 2006

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We prove some generic properties for C r , r = 1,2,. . .,∞, area-preserving 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 [10] on S 2 to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.",

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AB - We prove some generic properties for C r , r = 1,2,. . .,∞, area-preserving 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 [10] on S 2 to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.

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