Groups, Geometry, and Dynamics

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Volume 11, Issue 3, 2017, pp. 1103–1112
DOI: 10.4171/GGD/423

Published online: 2017-08-22

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

Mark C. Bell[1] and Saul Schleimer[2]

(1) University of Illinois at Urbana-Champaign, Urbana, USA
(2) University of Warwick, UK

Note by the authors: This article is in the public domain.

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.

Keywords: Pseudo-Anosov, laminations, rate of convergence

Bell Mark, Schleimer Saul: Slow north-south dynamics on $\mathcal {PML}$. Groups Geom. Dyn. 11 (2017), 1103-1112. doi: 10.4171/GGD/423