2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174458We consider Smale spaces, a particular class of hyperbolic topological dynamical systems, which include the basic sets for Smale's Axiom A systems. We present a homology theory for such systems which is based on the dimension group in the special case of shifts of finite type. This theory provides a Lefschetz formula relating trace data with the number of periodic points of the system.Research summary; complete version in preparation. The new version gives a substantially simplified and more natural definitionDynamical Systems37C70, 37D20, 37B10text