Topological entropy of free product automorphisms

Institute for Mathematical Physics Topological Entropy of Some Automorphisms of Reduced Amalgamated Free Product C {algebras

Topological Entropy of Some Automorphisms of Reduced Amalgamated Free Product C–algebras

Certain classes of automorphisms of reduced amalgamated free products of C∗– algebras are shown to have Brown–Voiculescu topological entropy zero. Also, for automorphisms of exact C∗–algebras, the Connes–Narnhofer–Thirring entropy is shown to be bounded above by the Brown–Voiculescu entropy. These facts are applied to generalize Størmer’s result about the entropy of automorphisms of the II1–fac...

TOPOLOGICAL ENTROPY OF SOME AUTOMORPHISMS OFREDUCED AMALGAMATED FREE PRODUCT C { ALGEBRASKenneth

Automorphisms of Hyperkähler Manifolds in the View of Topological Entropy

First we show that any group of automorphisms of null-entropy of a projective hyperkähler manifold M is almost abelian of rank at most ρ(M) − 2. We then characterize automorphisms of a K3 surface with nullentropy and those with positive entropy in algebro-geometric terms. We also give an example of a group of automorphisms which is not almost abelian in each dimension.

The Topological Version of Free Entropy

Notions of topological free entropy and of free capacity are introduced in the C∗algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.