Chaotic homeomorphisms on manifolds
โ Scribed by Aarts, Jan M. (author);Daalderop, Fons G.M. (author)
- Publisher
- Elsevier
- Year
- 1999
- Tongue
- English
- Weight
- 46 KB
- Volume
- 96
- Category
- Article
- ISSN
- 0166-8641
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โฆ Synopsis
For n 2, every n-dimensional compact manifold X admits a chaotic homeomorphism. The set of all chaotic measure-preserving homeomorphisms on X is dense in the space of all measurepreserving homeomorphisms.
๐ SIMILAR VOLUMES
Let ยต be a locally positive Borel measure on a ฯ -compact n-manifold X, n 2. We show that there is always a ยต-preserving homeomorphism of X which is maximally chaotic in that it satisfies Devaney's definition of chaos, with the sensitivity constant chosen maximally. Furthermore, maximally chaotic ho
The set of all chaotic measure-preserving homeomorphisms on a compact n-dimensional manifold (n 2) is a residual set in the space of all measure-preserving homeomorphisms.
We construct chaotic actions of certain finitely generated infinite abelian groups on evendimensional spheres, and of finite index subgroups of SL n (Z) on tori. We also study chaotic group actions via compactly supported homeomorphisms on open manifolds.