  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.
