区间上的分段收缩映射:Hausdorff维数、熵和吸引子

Pub Date : 2023-09-21 DOI:10.4153/s0008439523000747

Alfredo E. Calderón, Edgardo Villar-Sepúlveda

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引用次数: 0

摘要

摘要考虑在紧区间上定义的分段收缩映射f的吸引子。如果f是内射，我们证明可以通过与系统轨道相关的复杂性来估计f的拓扑熵(根据Bowen公式)和$\Lambda $的Hausdorff维数。具体地说，我们证明这两个数都是零。

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Piecewise contracting maps on the interval: Hausdorff dimension, entropy and attractors

Abstract We consider the attractor $\Lambda $ of a piecewise contracting map f defined on a compact interval. If f is injective, we show that it is possible to estimate the topological entropy of f (according to Bowen’s formula) and the Hausdorff dimension of $\Lambda $ via the complexity associated with the orbits of the system. Specifically, we prove that both numbers are zero.

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