Entropy vs volume for pseudo-Anosov maps
Geometric Topology
2008-12-17 v1 Dynamical Systems
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 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.
Cite
@article{arxiv.0812.2941,
title = {Entropy vs volume for pseudo-Anosov maps},
author = {Eiko Kin and Sadayoshi Kojima and Mitsuhiko Takasawa},
journal= {arXiv preprint arXiv:0812.2941},
year = {2008}
}
Comments
16 pages, 14 figures