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

13 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

Access to Document

10.1007/s00220-005-1514-3

Cite this

@article{1880536fa61b4540806b48834b490999,

title = "Area-preserving surface diffeomorphisms",

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.",

author = "Zhihong Xia",

year = "2006",

month = may,

doi = "10.1007/s00220-005-1514-3",

language = "English (US)",

volume = "263",

pages = "723--735",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Area-preserving surface diffeomorphisms

AU - Xia, Zhihong

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.

UR - http://www.scopus.com/inward/record.url?scp=33645291754&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645291754&partnerID=8YFLogxK

U2 - 10.1007/s00220-005-1514-3

DO - 10.1007/s00220-005-1514-3

M3 - Article

AN - SCOPUS:33645291754

SN - 0010-3616

VL - 263

SP - 723

EP - 735

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

Area-preserving surface diffeomorphisms

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this