Hyperbolic dynamical systems and Markov chains

This project studies the measure-valued Markov chains on hyperbolic dynamical systems, in particular the conditional probability measure process on self-conformal iterated function systems. Topics include local entropy averages, projections and slices, as well as fractal percolations. The project involves with compact group extension theory for Dynamical Systems, Markov chains for Probability Theory and dimension theory for Fractal Geometry.