Order on the homology groups of Smale spaces (Q2397669)

Smale spaces introduced by \textit{D. Ruelle} [Thermodynamic formalism. The mathematical structures of classical equilibrium. Statistical mechanics. With a foreword by Giovanni Gallavotti. Encyclopedia of Mathematics and its Applications. Vol. 5. Reading, Massachusetts: Addison-Wesley Publishing Company. (1978; Zbl 0401.28016)] are topological dynamical systems that model hyperbolic behavior. The authors show that the homology groups on Smale spaces (in degree zero) have a canonical order structure.