M. Braverman is an expert in Theoretical Computer Science, particularly in applications of computability to Complex Analysis and Dynamical Systems M. Yampolsky is an expert in Dynamical Systems, particularly in Holomorphic Dynamics and Renormalization Theory

• to Computability.- Dynamics of Rational Mappings.- First Examples.- Positive Results.- Negative Results.- Computability versus Topological Properties of Julia Sets.

From the reviews: "The study of dynamical systems has at its core ... a very computational feel. ... One can feel the book trying to be self-contained ... . The subject of the book is timely and important. ... The questions posed and answered in the present book are natural and the approach well-suited to produce enlightening results. ... The book is also generous ... . It has the potential to inspire considerable future work in this intriguing field." (Wesley Calvert, SIGACT News, Vol. 41 (1), 2010) "Written in an accessible way with many explications, examples and illustrations. ... this book sees the meeting of two worlds: computability theory and iteration of rational maps. It is a fruitful one ... and a share of surprises. It is also a compendium of several years of research by the authors ... together with a lot of new results. ... a nice and quick introduction to both topics, and much of it is pleasant to read ... . includes interesting discussions and presents stimulating conjectures." (Arnaud Cheritat, Foundations of Computational Mathematics, Vol. 12, 2012)