Distributions of periodic points for the Dyck shift and the heterochaos baker maps

2024/09/02 by Hiroki Takahasi, Takahasi, Hiroki
Mathematics · #advanced mathematical theories #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2409.01261

Abstract

The heterochaos baker maps are piecewise affine maps on the square or the cube that are one of the simplest partially hyperbolic systems. The Dyck shift is a well-known example of a subshift that has two fully supported ergodic measures of maximal entropy (MMEs). We show that the two ergodic MMEs of the Dyck shift are represented as asymptotic distributions of sets of periodic points of different multipliers. We transfer this result to the heterochaos baker maps, and show that their two ergodic MMEs are represented as asymptotic distributions of sets of periodic points of different unstable dimensions.

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