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arXiv · 2209.05019

Explicit Dynamical Systems on the Sierpi\'nski Curve

Worapan Homsomboon
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Abstract

We apply Boro\'nski and Oprocha's inverse limit construction of dynamical systems on the Sierpi\'nski carpet by using the initial systems of $n-$Chamanara surfaces and their $n-$baker transformations, $n \geq 2$. We show that all positive real numbers are realized as metric entropy values of dynamical systems on the carpet. We also produce a simplification of Boro\'nski and Oprocha's proof showing that dynamical systems on the carpet do not have the Bowen specification property.

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Worapan Homsomboon. 2022-09-12. Explicit Dynamical Systems on the Sierpi\'nski Curve. https://arxiv.org/abs/2209.05019

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