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Addendum to “Limit Sets of Typical Homeomorphisms”

Published online by Cambridge University Press:  20 November 2018

Nilson C. Bernardes Jr.
Nilson C. Bernardes Jr.*
Affiliation:
Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa POstal 68530, Rio de Janeiro, RJ, 21945-970, Brasil e-mail: bernardes@im.ufrj.br
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Abstract

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Given an integer $n\,\ge \,3$, 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 $\omega \left( f,\,x \right)$ (respectively to the alpha limit set $\alpha \left( f,\,x \right)$) is topologically conjugate to the universal odometer.

Keywords

37B2054H2028C1554C3554E52topological manifoldshomeomorphismsmeasuresBaire categorylimit sets
Type
Addendum
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 2 , 14 June 2014 , pp. 240 - 244
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

The author was partially supported by CAPES: Bolsista - Proc. no BEX 4012/11-9.

References

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