- journal article metadata
European Mathematical Society Publishing House
2017-08-25 23:45:01
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2017
3
Slow north-south dynamics on $\mathcal {PML}$
Mark
Bell
University of Illinois at Urbana-Champaign, Urbana, USA
Saul
Schleimer
University of Warwick, UK
Pseudo-Anosov, laminations, rate of convergence
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.
Dynamical systems and ergodic theory
Manifolds and cell complexes
1103
1112
10.4171/GGD/423
http://www.ems-ph.org/doi/10.4171/GGD/423