Dynamical degrees of birational transformations of projective surfaces

Abstract

ABSTRACT. The dynamical degree λ ( f) of a birational transformation f measures the exponential growth rate of the degree of the formulae that de-fine the n-th iterate of f. We study the set of all dynamical degrees of all bi-rational transformations of projective surfaces, and the relationship between the value of λ ( f) and the structure of the conjugacy class of f. For instance, the set of all dynamical degrees of birational transformations of the complex projective plane is a closed, well ordered set of algebraic numbers. 1.