Explicit Dynamical Systems on the Sierpiński Curve

2022/09/12 by Homsomboon, Worapan
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.05019

Abstract

We apply Boroński and Oprocha's inverse limit construction of dynamical systems on the Sierpiński carpet by using the initial systems of n-Chamanara surfaces and their n-baker transformations, n ≥ 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 Boroński and Oprocha's proof showing that dynamical systems on the carpet do not have the Bowen specification property.

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