Small dilatation pseudo-Anosov mapping classes and short circuits on train track automata

Abstract

This note gives a brief survey of the minimum dilatation problem for pseudo-Anosov mapping classes, and the first explicit train track description of an infinite family of pseudo-Anosov mapping classes with orientable stable foliations and the conjectural minimum dilatation for closed surfaces of even genus $g\ge 2$.

25 pages, 11 figures. Will be included in the Institut Mittag-Leffler preprint series, Workshop on Mahler Measure and Growth in Geometry and Topology (2013)

References in corpus (4)

• A family of pseudo-Anosov braids with small dilatation
• Small dilatation pseudo-Anosovs and 3-manifolds
• Minimal dilatations of pseudo-Anosovs generated by the magic 3-manifold and their asymptotic behavior
• On pseudo-Anosov mapping classes with minimum dilatation and Lanneau-Thiffeault numbers

Cited by in corpus (1)

• Dynamics of the monodromies of the fibrations on the magic 3-manifold