Ergodicity and Annular Homeomorphisms of the Torus

被引：3

作者：

Bortolatto, Renato B. ^{[1
]}

Tal, Fabio A. ^{[1
]}

机构：

[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, Brazil

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2013年 / 12卷 / 02期

关键词：

Torus homeomorphisms; Rotation sets; Ergodicity; Periodic points; ROTATION VECTORS; RECURRENCE; POINTS; SETS;

D O I：

10.1007/s12346-012-0095-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let f : T-2 -> T-2 be a homeomorphism homotopic to the identity and F : R-2 -> R-2 a lift of f such that the rotation set rho(F) is a line segment of rational slope containing a point in Q(2). We prove that if f is ergodic with respect to the Lebesgue measure on the torus and the average rotation vector (with respect to same measure) does not belong to Q(2) then some power of f is an annular homeomorphism.

引用

页码：377 / 391

页数：15

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