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arXiv · 1307.0361

Dynamical degrees of birational transformations of projective surfaces

Jérémy Blanc·Serge Cantat
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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 formulae 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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Jérémy Blanc, Serge Cantat. 2013-07-01. Dynamical degrees of birational transformations of projective surfaces. https://doi.org/10.1090/jams831

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