The ordinal of dynamical degrees of birational maps of the projective plane

TL;DR

This paper proves that the set of dynamical degrees of all complex birational maps of the projective plane has an ordinal type of , revealing a precise ordinal classification.

Contribution

It establishes that the ordinal of the dynamical degrees for all such maps is exactly , providing a complete ordinal characterization.

Findings

The ordinal of the dynamical degrees is .

The result applies to all complex birational maps of the projective plane.

The proof involves ordinal analysis of the dynamical degrees.

Abstract

We show that the ordinal of the dynamical degrees of all complex birational maps of the projective plane is $\omega^\omega$.