Journal of Modern Dynamics (JMD)

An algebraic characterization of expanding Thurston maps

Pages: 451 - 476, Issue 4, October 2012      doi:10.3934/jmd.2012.6.451

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Peter Haïssinsky - Université Paul Sabatier, Institut de Mathématiques de Toulouse (IMT), 118 route de Narbonne, 31062 Toulouse Cedex 9, France (email)
Kevin M. Pilgrim - Dept. Mathematics, Indiana University, Bloomington, IN 47405, United States (email)

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 $g$.

Keywords:  Thurston map, virtual endomorphism, expanding.
Mathematics Subject Classification:  Primary: 37F20; Secondary: 37D20, 20E08, 20F65, 54E40.

Received: May 2012;      Available Online: January 2013.