Entropy-minimizing diffeomorphisms of pseudo-Anosov type on K3 surfaces

TL;DR

This paper constructs entropy-minimizing pseudo-Anosov type diffeomorphisms on K3 surfaces, providing infinitely many examples that do not preserve any complex structure, thus advancing understanding of surface dynamics and complex geometry.

Contribution

It introduces a method to construct entropy-minimizing pseudo-Anosov diffeomorphisms on K3 surfaces that lack any compatible complex structure.

Findings

Infinitely many such diffeomorphisms exist.

These diffeomorphisms do not preserve any complex structure.

They minimize entropy within their homotopy class.

Abstract

We construct diffeomorphisms of ``pseudo-Anosov type'' on K3 surfaces M. In particular we obtain infinitely many examples of such diffeomorphisms that minimize entropy in their homotopy class, and for which neither the diffeomorphism nor any diffeomorphism homotopic to it preserves any complex structure on M.