Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy

Symplectic Automorphisms on Kummer Surfaces

Nikulin proved that the isometries induced on the second cohomology group of a K3 surface X by a finite abelian group G of symplectic automorphisms are essentially unique. Moreover he computed the discriminant of the sublattice of H(X,Z) which is fixed by the isometries induced by G. However for certain groups these discriminants are not the same of those found for explicit examples. Here we de...

Measures of maximal entropy

We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.

Periodic Automorphisms of Surfaces: Invariant Circles and Maximal Orders

CONTENTS

Isomorphism Rigidity of Commuting Automorphisms

Let d > 1, and let (X,α) and (Y, β) be two zeroentropy Z-actions on compact abelian groups by d commuting automorphisms. We show that if all lower rank subactions of α and β have completely positive entropy, then any measurable equivariant map from X to Y is an affine map. In particular, two such actions are measurably conjugate if and only if they are algebraically conjugate.

Automorphisms of projective K3 surfaces with minimum entropy