TY - JOUR
T1 - Area-preserving surface diffeomorphisms
AU - Xia, Zhihong
N1 - Copyright:
Copyright 2006 Elsevier B.V., All rights reserved.
PY - 2006/5
Y1 - 2006/5
N2 - 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.
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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U2 - 10.1007/s00220-005-1514-3
DO - 10.1007/s00220-005-1514-3
M3 - Article
AN - SCOPUS:33645291754
VL - 263
SP - 723
EP - 735
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 3
ER -