Transitivity and rotation sets with nonempty interior for homeomorphisms of the 2-torus (Q2845873)
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scientific article; zbMATH DE number 6204063
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Transitivity and rotation sets with nonempty interior for homeomorphisms of the 2-torus |
scientific article; zbMATH DE number 6204063 |
Statements
3 September 2013
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torus homeomorphism
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rotation set
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omega limit
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Transitivity and rotation sets with nonempty interior for homeomorphisms of the 2-torus (English)
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The main result of the paper states that if \(f\) is a homeomorphism of the \(2\)-torus isotopic to the identity for which there exists an \(x_0\in \mathbb{R}^2\) such that the omega limit of the orbit of \(x_0\) by a lift of \(f\) contains all \(\mathbb{Z}^2\) translates of \(x_0\), then \((0, 0)\) is in the interior of the rotation set of the lift.
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