G.G. Emch, H. Narnhofer, G.L. Sewell, W. Thirring
Anosov Actions on Non--Commutative Algebras
(60K, LaTeX)

ABSTRACT.  We construct an axiomatic framework for a quantum mechanical
extension to the theory of Anosov systems, and show that this
retains some of the characteristic features of its classical
counterpart, e.g. positive Lyapunov exponents,  a vectorial
K--property, and exponential clustering. We then investigate 
the effects of quantisation on two prototype examples of Anosov 
systems, namely the iterations of an automorphism of the torus 
(the `Arnold Cat' model) and the free dynamics of a particle on 
a surface of negative curvature. It emerges that the
Anosov property survives quantisation in the case of the former
model, but not of the latter one. Finally, we show that the
modular dynamics of a relativistic quantum field on the Rindler
wedge of Minkowski space is that of an Anosov system.