Entropy vs volume for pseudo-Anosov maps

Details Entropy vs volume for pseudo-Anosov maps Entropy vs volume for pseudo-Anosov maps

2008-12-15

arxiv.org/abs/0812.2941v1

Mathematics

Geometric Topology

16 pages, 14 figures

Scientific paper

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 Teichm\"uller 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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