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