Topological Entropy of Pseudo-Anosov Maps from a Typical Thurston’s Construction

Autor:	Dongryul M. Kim, Hyungryul Baik, Inhyeok Choi
Rok vydání:	2021
Předmět:	Moment (mathematics) Pure mathematics Monodromy Rank (linear algebra) General Mathematics Free group Mapping torus Topological entropy Random walk Mathematics::Geometric Topology Hyperbolic volume Mathematics
Zdroj:	International Mathematics Research Notices. 2022:19862-19904
ISSN:	1687-0247 1073-7928
DOI:	10.1093/imrn/rnab167
Popis:	In this paper, we develop a way to extract information about a random walk associated with a typical Thurston’s construction. We first observe that a typical Thurston’s construction entails a free group of rank 2. We also present a proof of the spectral theorem for random walks associated with Thurston’s construction that have finite 2nd moment with respect to the Teichmüller metric. Its general case was remarked by Dahmani and Horbez. Finally, under a hypothesis not involving moment conditions, we prove that random walks eventually become pseudo-Anosov. As an application, we first discuss a random analogy of Kojima and McShane’s estimation of the hyperbolic volume of a mapping torus with pseudo-Anosov monodromy. As another application, we discuss non-probabilistic estimations of stretch factors from Thurston’s construction and the powers for Salem numbers to become the stretch factors of pseudo-Anosovs from Thurston’s construction.
Databáze:	OpenAIRE
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