Georgia Institute of Technology College of Sciences

Let f be a rational self-map of the complex projective plane. A central problem when analyzing the dynamics of f is to understand the sequence of degrees deg(f^n) of the iterates of f. Knowing the growth rate and structure of this sequence in many cases enables one to construct invariant currents/measures for dynamical system as well as bound its topological entropy. Unfortunately, the structure of this sequence remains mysterious for general rational maps. Over the last ten years, however, an approach to the problem through studying dynamics on spaces of valuations has proved fruitful. In this talk, I aim to discuss the link between dynamics on valuation spaces and problems of degree/order growth in complex dynamics, and discuss some of the positive results that have come from its exploration.