Dynamical degrees of birational transformations of projective surfaces

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.

65 pages

Cited by in corpus (9)

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• Conjugacy classes of special automorphisms of the affine spaces
• The embeddings of the Heisenberg group into the Cremona group
• Dynamical degrees of automorphisms of complex simple abelian varieties and Salem numbers
• The degeneration of a family of rational surface automorphisms