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Lalley’s theorem on periodic orbits of hyperbolic flows. (English) Zbl 0915.58074
Summary: We give an asymptotic estimate for the number of periodic orbits of an Anosov flow which are subject to multidimensional constraints. We also study their spatial distribution. For instance, we describe the distribution of periodic orbits with respect to homology classes, for both homologically full Anosov flows and suspensions of Anosov transformations.

MSC:
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
37C10 Dynamics induced by flows and semiflows
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
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