Slow north-south dynamics on $\mathcal{PML}$

Mark C. Bell; Saul Schleimer

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arXiv · 1512.00829

Slow north-south dynamics on $\mathcal{PML}$

Mark C. Bell·Saul Schleimer

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Abstract

We consider the action of a pseudo-Anosov mapping class on $\mathcal{PML}(S)$. This action has north-south dynamics and so, under iteration, laminations converge exponentially to the stable lamination. We study the rate of this convergence and give examples of families of pseudo-Anosov mapping classes where the rate goes to one, decaying exponentially with the word length. Furthermore we prove that this behaviour is the worst possible.

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Mark C. Bell, Saul Schleimer. 2015-12-02. Slow north-south dynamics on $\mathcal{PML}$. https://arxiv.org/abs/1512.00829

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