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Addendum to “Limit Sets of Typical Homeomorphisms”
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 2 / 14 June 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 240-244
- Print publication:
- 14 June 2014
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- Article
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- You have access
- Export citation
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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.
Limit Sets of Typical Homeomorphisms
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- Journal:
- Canadian Mathematical Bulletin / Volume 55 / Issue 2 / 01 June 2012
- Published online by Cambridge University Press:
- 20 November 2018, pp. 225-232
- Print publication:
- 01 June 2012
-
- Article
-
- You have access
- Export citation
-
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 limit set 
$\omega (f,\,x)$ is a Cantor set of Hausdorff dimension zero, each point of $\omega (f,\,x)$ has a dense orbit in $\omega (f,\,x)$, 
$f$ is non-sensitive at each point of $\omega (f,\,x)$, and the function 
$a\,\to \,\omega (f,\,a)$ is continuous at $x$.
