New Fibonacci-Like Wild Attractors for Unimodal Interval Maps

Abstract

This thesis focuses on the existence of wild Cantor attractors of unimodal interval maps. It was shown that unimodal interval maps with Fibonacci combinatorics and high criticality have wild attractors by Bruin, Keller, Nowicki and van Strien and the result was later generalized by Bruin to a so-called Fibonacci-like class of maps. In this thesis, we provide new examples of unimodal interval maps which possess wild attractors but are different from the class considered by Bruin. The methods here include Real Koebe Principle, renormalization theory and absolutely continuous invariant measure of Markov map.