- Experiment. Math.
- Volume 18, Issue 4 (2009), 397-407.
Entropy versus Volume for Pseudo-Anosovs
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.
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
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