Uniformly scaled Markov partitions for unimodal maps (Q1125646)

This paper deals with uniformly scaled Markov partitions for unimodal maps. More precisely the author constructs uniformly scaled partitions for unimodal maps of the interval which admits a straightforward 2-dimensional generalization. The author proceeds by induction. To start the inductive process, he performs a special preliminary construction, in the phase space, of a strongly hyperbolic set of large relative measure. The main result of the author states that there exists a set of positive measure of parameter values with absolutely continuous invariant measures and uniformly scaled Markov partitions.