Expand all Collapse all | Results 1 - 5 of 5 |
1. CMB 2012 (vol 57 pp. 240)
Addendum to ``Limit Sets of Typical Homeomorphisms'' 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 Categories:37B20, 54H20, 28C15, 54C35, 54E52 |
2. CMB 2011 (vol 55 pp. 225)
Limit Sets of Typical Homeomorphisms 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
$f \colon X \to X$, 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 $x$.
Keywords:topological manifolds, homeomorphisms, measures, Baire category, limit sets Categories:37B20, 54H20, 28C15, 54C35, 54E52 |
3. CMB 2011 (vol 55 pp. 157)
Subdivisions of Simplicial Complexes Preserving the Metric Topology Let $|K|$ be the metric polyhedron of a simplicial complex $K$.
In this paper,
we characterize a simplicial subdivision $K'$ of $K$
preserving the metric topology for $|K|$ as the one such that
the set $K'{}^{(0)}$ of vertices of $K'$ is discrete in $|K|$.
We also prove that two such subdivisions of $K$
have such a common subdivision.
Keywords:metric topology, simplicial complex, admissible (or proper) subdivision, admissible PL homeomorphism |
4. CMB 2010 (vol 53 pp. 438)
Near-Homeomorphisms of Nöbeling Manifolds We characterize maps between $n$-dimensional NÃ¶beling manifolds that can be approximated by homeomorphisms.
Keywords:n-dimensional Nöbeling manifold, Z-set unknotting, near-homeomorphism Categories:55M10, 54F45 |
5. CMB 2000 (vol 43 pp. 343)
Controlled Homeomorphisms Over Nonpositively Curved Manifolds We obtain a homotopy splitting of the forget control map for
controlled homeomorphisms over closed manifolds of nonpositive
curvature.
Keywords:controlled topology, controlled homeomorphism, nonpositive curvature, Novikov conjectures Categories:57N15, 53C20, 55R65, 57N37 |