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

Clark, Trevor (2014). Regular or stochastic dynamics in families of higher-degree unimodal maps. Ergodic Theory and Dynamical Systems, 34(5) pp. 1538–1566.

DOI: https://doi.org/10.1017/etds.2013.10

Abstract

We construct a lamination of the space of unimodal maps with critical points of fixed degree 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.

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