Experimental Mathematics

Entropy versus Volume for Pseudo-Anosovs

E. Kin, S. Koijima, and M. Takasawa

Full-text: Open access


We discuss a comparison of the entropy of pseudo-Anosov maps 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.

Article information

Experiment. Math., Volume 18, Issue 4 (2009), 397-407.

First available in Project Euclid: 25 November 2009

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces 57M27: Invariants of knots and 3-manifolds
Secondary: 57M55

Mapping class group braid group pseudo-Anosov dilatation entropy hyperbolic volume


Kin, E.; Koijima, S.; Takasawa, M. Entropy versus Volume for Pseudo-Anosovs. Experiment. Math. 18 (2009), no. 4, 397--407. https://projecteuclid.org/euclid.em/1259158505

Export citation