Accessibility of the Thurston Set

This lecture explores the accessibility of the boundary of the Thurston set, discussing the history of its study, motivations behind discerning holes in the set, and the self-similarity properties of the attractor. The main results focus on the accessibility of certain parameters within the set, with theorems proving the accessibility of specific points. The idea of proof involves using asymptotic similarity and iterative constructions. Notations and conditions on Taylor polynomials are detailed, along with examples demonstrating the application of the theorems. Open questions are posed regarding the density of certain parameters in the set and their association with Misiurewicz parameters.