Entropy vs volume for pseudo-Anosov maps

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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.
16 pages, 14 figures

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Geometric Topology, Dynamical Systems, 37E30, 57M27, 57M55

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http://salesiana.dossiersoluciones.com/handle/123456789/210733

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0812.2941
 http://arxiv.org/abs/0812.2941

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arXiv