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Regular or stochastic dynamics in families of higher-degree unimodal maps

Published online by Cambridge University Press:  03 April 2013

TREVOR CLARK
TREVOR CLARK*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, USA email [email protected]
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Abstract

We construct a lamination of the space of unimodal maps with critical points of fixed degree $d\geq 2$ by the hybrid classes. The structure of the lamination yields a partition of the parameter space for one-parameter real analytic families of unimodal maps and allows us to transfer a priori bounds in the phase space to the parameter space. This implies that almost every map in such a family is either regular or stochastic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 5 , October 2014 , pp. 1538 - 1566
Copyright
Copyright ©2013 Cambridge University Press 

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