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arXiv · 1303.3099

Transitive cylinder flows whose set of discrete points is of full Hausdorff dimension

Eugeniusz Dymek
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Abstract

For each irrational $\alpha\in[0,1)$ we construct a continuous function $f\: [0,1)\to \R$ such that the corresponding cylindrical transformation $[0,1)\times\R \ni (x,t) \mapsto (x+\alpha, t+ f(x)) \in [0,1)\times\R$ is transitive and the Hausdorff dimension of the set of points whose orbits are discrete is 2. Such cylindrical transformations are shown to display a certain chaotic behaviour of Devaney-like type.

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Eugeniusz Dymek. 2013-03-13. Transitive cylinder flows whose set of discrete points is of full Hausdorff dimension. https://arxiv.org/abs/1303.3099

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