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arXiv · 2206.09601

Density of periodic measures and large deviation principle for generalized $(\alpha, \beta)$-transformations

Mao Shinoda·Kenichiro Yamamoto
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Abstract

We introduce generalized $(\alpha,\beta)$-transformations, which include all $(\alpha,\beta)$ and generalized $\beta$-transformations, and prove that all transitive generalized $(\alpha,\beta)$-transformations satisfy the level-2 large deviation principle with a unique measure of maximal entropy. A crucial step in our proof is to establish density of periodic measures in the set of ergodic measures.

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Mao Shinoda, Kenichiro Yamamoto. 2022-06-20. Density of periodic measures and large deviation principle for generalized $(\alpha, \beta)$-transformations. https://arxiv.org/abs/2206.09601

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