Twist-wise flow equivalence
by
Mike Sullivan
Southern Illinois University at Carbondale
Coauthors: Mike Boyle

We consider directed graphs with labels from a finite group G. These define skew product systems of shifts of finite type over G. Notions of topological conjugacy and topological equivalence of suspension flows can be generalized to cover these systems, where incidence matrices now take entries from the semi-group ring Z₊[G]. Using ideas from K-theory the classification problems can be greatly simplified. For G=Z/2 we report on progress made in classifying square irreducible matrices over the ring Z[Z/2] up to twist-wise flow equivalence. This was motivated by the desire to include information about the twisting of stable manifolds of orbits in basic sets of Smale flows in the symbolic dynamics models.

Date received: February 6, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajz-19.