# American Institute of Mathematical Sciences

October  2012, 6(4): 451-476. doi: 10.3934/jmd.2012.6.451

## An algebraic characterization of expanding Thurston maps

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

Received  May 2012 Published  January 2013

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 $g$.
Citation: Peter Haïssinsky, Kevin M. Pilgrim. An algebraic characterization of expanding Thurston maps. Journal of Modern Dynamics, 2012, 6 (4) : 451-476. doi: 10.3934/jmd.2012.6.451
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