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

摘要

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