Entropy vs volume for pseudo-Anosov maps

Eiko Kin; Sadayoshi Kojima; Mitsuhiko Takasawa

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arXiv · 0812.2941

Entropy vs volume for pseudo-Anosov maps

Eiko Kin·Sadayoshi Kojima·Mitsuhiko Takasawa

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Abstract

We will discuss theoretical and experimental results concerning comparison of entropy of pseudo-Anosov maps and volume of their mapping tori. Recent study of Weil-Petersson geometry of the Teichmüller space tells us that they admit linear inequalities for both sides under some bounded geometry condition. We construct a family of pseudo-Anosov maps which violates one side of inequalities under unbounded geometry setting, present an explicit bounding constant for a punctured torus, and provide several observations based on experiments.

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Eiko Kin, Sadayoshi Kojima, Mitsuhiko Takasawa. 2008-12-15. Entropy vs volume for pseudo-Anosov maps. https://arxiv.org/abs/0812.2941

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