AN ANALOGUE OF BAUER’S THEOREM FOR CLOSED ORBITS OF SKEW PRODUCTS

Let φ: X → X be a hyperbolic dynamical system and, for a finite G, let �φ: � X → � X be a G-extension for which � φ is also hyperbolic. Given φ we are interested in describing the possibilities for � φ in terms of the closed φ orbits. This is analogous to a classical problem in number theory which asks for