An algebraic characterization of expanding Thurston maps

Peter Haïssinsky; Kevin M. Pilgrim

doi:10.3934/jmd.2012.6.451

Article Contents

2012, Volume 6, Issue 4: 451-476. Doi: 10.3934/jmd.2012.6.451

This issue Previous Article Weak mixing suspension flows over shifts of finite type are universal Next Article Ergodic infinite group extensions of geodesic flows on translation surfaces

An algebraic characterization of expanding Thurston maps

Peter Haïssinsky^1, and
Kevin M. Pilgrim^2,

1.
Université Paul Sabatier, Institut de Mathématiques de Toulouse (IMT), 118 route de Narbonne, 31062 Toulouse Cedex 9
2.
Dept. Mathematics, Indiana University, Bloomington, IN 47405

Received: April 30, 2012

Published: December 2012

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Abstract

Let $f\colon S^2 \to S^2$ be a postcritically finite branched covering map without periodic branch points. We give necessary and sufficient algebraic conditions for $f$ to be homotopic, relative to its postcritical set, to an expanding map $g$.

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Mathematics Subject Classification: Primary: 37F20; Secondary: 37D20, 20E08, 20F65, 54E40.

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