CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Addendum to ``Limit Sets of Typical Homeomorphisms''

  Published:2012-11-13
 Printed: Jun 2014
  • Nilson C. Bernardes Jr.,
    Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, 21945-970, Brasil
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   LaTeX   MathJax   PDF  

Abstract

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 $f : X \to X$, 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 topologically conjugate to the universal odometer.
Keywords: topological manifolds, homeomorphisms, measures, Baire category, limit sets topological manifolds, homeomorphisms, measures, Baire category, limit sets
MSC Classifications: 37B20, 54H20, 28C15, 54C35, 54E52 show english descriptions Notions of recurrence
Topological dynamics [See also 28Dxx, 37Bxx]
Set functions and measures on topological spaces (regularity of measures, etc.)
Function spaces [See also 46Exx, 58D15]
Baire category, Baire spaces
37B20 - Notions of recurrence
54H20 - Topological dynamics [See also 28Dxx, 37Bxx]
28C15 - Set functions and measures on topological spaces (regularity of measures, etc.)
54C35 - Function spaces [See also 46Exx, 58D15]
54E52 - Baire category, Baire spaces
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/