Periodic points of birational maps on projective surfaces

TL;DR

This paper classifies birational maps on smooth projective surfaces with dense non-critical periodic points, showing that a first dynamical degree greater than one guarantees Zariski density of periodic points.

Contribution

It provides a classification of such maps and establishes a condition linking the dynamical degree to the density of periodic points.

Findings

Periodic points are Zariski dense when the first dynamical degree exceeds one.

Classification of birational maps with dense periodic points.

Connection between dynamical degree and periodic point distribution.

Abstract

We classify birational maps of projective smooth surfaces whose non-critical periodic points are Zariski dense. In particular, we show that if the first dynamical degree is greater than one, then the periodic points are Zariski dense.