Addendum to ``Limit Sets of Typical Homeomorphisms'

Canadian mathematical bulletin

Nilson C. Bernardes Jr.¹ 

[1]Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, 21945-970, Brasil

关键词: topological manifolds;    homeomorphisms;    measures;    Baire category;    limit sets;   

DOI  :  10.4153/CMB-2012-033-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Given an integer $n geq 3$,a metrizable compact topological $n$-manifold $X$ with boundary,and a finite positive Borel measure $mu$ on $X$,we prove that for the typical homeomorphism $f : X o X$,it is true that for $mu$-almost every point $x$ in $X$ the restriction of$f$ (respectively of $f^{-1}$) to the omega limit set $omega(f,x)$(respectively to the alpha limit set $alpha(f,x)$) is topologicallyconjugate to the universal odometer.

【 授权许可】

Unknown