Dynamical degrees

Dynamical degrees

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Serge Cantat , Université de Rennes I

Let f be a birational transformation of the projective plane. The degree deg(f) is the degree of the image of a generic line by f. The dynamical degree of f captures the exponential growth rate of the sequence deg(f^n), where f^n denotes the n-th iterate of f. The structure of the set of dynamical degrees of all birational transformations of the plane is quite interesting ; for instance, it is a well ordered subset of famous algebraic integers, namely Salem and Pisot numbers . (this is joint work with Jérémy Blanc)