Suggested reading:
Introduction to dynamical systems, by M. Brin and G. Stuck.
An introduction to ergodic theory, by P. Walters.
Fractal geometry- mathematical foundations and applications, by K. Falconer.
More resources:
Introduction to the modern theory of dynamical systems, by A. Katok and B. Hasselblatt.
Dynamics in one complex variable, by J. Milnor.
Hausdorff measures, by C. A. Rogers.
Conformal fractals- ergodic theory methods, by F. Przytycki and M. Urbanski.
Problem sets: