Small dilatation pseudo-Anosov mapping classes and short circuits on   train track automata
  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 $g \ge 2$. 
Eriko Hironaka
math.GT