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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 $g \ge 2$.

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