The ordinal of dynamical degrees

The birational automorphism $f$ of a smooth surface acts on the Neron-Severi group of the surface as a linear operator $f^*$. The iterates $(f^n)^*$ grows exponentially i.e. as $\lambda^n$. The base $\lambda$ is called the dynamical degree of $f$. It is a positive real number. Moreover, if we fix a surface then the set of all dynamical degrees of its automorphisms is well-ordered. In my talk I am going to describe the ordinal of this set. The talk is based on the paper "The ordinal of dynamical degrees of birational maps of the projective plane" by Anna Bot.