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Continuous flows generate few homeomorphisms
Published online by Cambridge University Press: 25 August 2020
Abstract
We describe topological obstructions (involving periodic points, topological entropy and rotation sets) for a homeomorphism on a compact manifold to embed in a continuous flow. We prove that homeomorphisms in a $C^{0}$-open and dense set of homeomorphisms isotopic to the identity in compact manifolds of dimension at least two are not the time-1 map of a continuous flow. Such property is also true for volume-preserving homeomorphisms in compact manifolds of dimension at least five. In the case of conservative homeomorphisms of the torus
$\mathbb {T}^{d} (d\ge 2)$ isotopic to identity, we describe necessary conditions for a homeomorphism to be flowable in terms of the rotation sets.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 4 , November 2020 , pp. 971 - 983
- Copyright
- Copyright © The Author(s), 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society
References
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