JournalsjemsVol. 3 , No. 4pp. 287–333

Pruning theory and Thurston's classification of surface homeomorphisms

  • André de Carvalho

    State Univ of New York at Stony Brook, United States
  • Toby Hall

    University of Liverpool, United Kingdom
Pruning theory and Thurston's classification of surface homeomorphisms cover
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Abstract

Two dynamical deformation theories are presented - one for surface homeomorphisms, called pruning, and another for graph endomorphisms, called kneading - both giving conditions under which all of the dynamics in an open set can be destroyed, while leaving the dynamics unchanged elsewhere. The theories are related to each other and to Thurston's classification of surface homeomorphisms up to isotopy.

Cite this article

André de Carvalho, Toby Hall, Pruning theory and Thurston's classification of surface homeomorphisms. J. Eur. Math. Soc. 3 (2001), no. 4 pp. 287–333

DOI 10.1007/S100970100034