Entropy versus volume for pseudo-anosovs

E. Kin, S. Kojima, M. Takasawa

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We discuss a comparison of the entropy of pseudo-Anosovmaps and the volume of their mapping tori. Recent study of the Weil– Petersson geometry of Teichmüller space tells us that the entropy and volume admit linear inequalities for both directions under some bounded geometry condition. Based on experiments, we present various observations on the relation between minimal entropies and volumes, and on bounding constants for the entropy over the volume from below. We also provide explicit bounding constants for a punctured torus case.

Original languageEnglish
Pages (from-to)397-407
Number of pages11
JournalExperimental Mathematics
Volume18
Issue number4
DOIs
Publication statusPublished - 2009 Jan 1

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Keywords

  • Braid group
  • Dilatation
  • Entropy
  • Hyperbolic volume
  • Mapping class group
  • Pseudo-Anosov

ASJC Scopus subject areas

  • Mathematics(all)

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