American Institute of Mathematical Sciences

December  2006, 16(4): 883-896. doi: 10.3934/dcds.2006.16.883

The Thurston operator for semi-finite combinatorics

 1 Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brazil

Received  January 2006 Revised  May 2006 Published  September 2006

Given a continuous $l$-modal map $g$ of the interval $[0,1]$ we prove the existence of a polynomial $P$ with modality $\leq l$ such that $g$ is strongly semi-conjugate to $P$ in $[0,1]$. This is an improvement of a result in [4]. We do a modification on the Thurston operator in order to control the semi-finite combinatorial case. It turns out that all the essential attractors of $P$ have the same local topological type as those of $g$. This allows to construct the strong semi-conjugacy. We also present some examples agreeing with the results.
Citation: Pedro A. S. Salomão. The Thurston operator for semi-finite combinatorics. Discrete & Continuous Dynamical Systems - A, 2006, 16 (4) : 883-896. doi: 10.3934/dcds.2006.16.883
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