Geodesic
Pruning theory and Thurston's classification of surface homeomorphisms
Journal of the European Mathematical Society, Tome 3 (2001) no. 4, pp. 287-333.

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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.
DOI : 10.1007/s100970100034
Classification : 14-XX, 00-XX
Keywords: 
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     author = {Andr\'e de Carvalho and Toby Hall},
     title = {Pruning theory and {Thurston's} classification of surface homeomorphisms},
     journal = {Journal of the European Mathematical Society},
     pages = {287--333},
     publisher = {mathdoc},
     volume = {3},
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     year = {2001},
     doi = {10.1007/s100970100034},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970100034/}
}
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André de Carvalho; Toby Hall. Pruning theory and Thurston's classification of surface homeomorphisms. Journal of the European Mathematical Society, Tome 3 (2001) no. 4, pp. 287-333. doi : 10.1007/s100970100034. http://geodesic.mathdoc.fr/articles/10.1007/s100970100034/

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