Dynamical degrees of birational transformations of projective surfaces

Blanc, Jérémy; Cantat, Serge

doi:10.1090/jams831

Dynamical degrees of birational transformations of projective surfaces
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by Jérémy Blanc and Serge Cantat

J. Amer. Math. Soc. 29 (2016), 415-471

DOI: https://doi.org/10.1090/jams831

Published electronically: June 3, 2015

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Abstract:

The dynamical degree $\lambda (f)$ of a birational transformation $f$ measures the exponential growth rate of the degree of the formulas that define the $n$th iterate of $f$. We study the set of all dynamical degrees of all birational transformations of projective surfaces, and the relationship between the value of $\lambda (f)$ 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 and well ordered set of algebraic numbers.

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