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Some compact invariant sets for hyperbolic linear automorphisms of torii. (English) Zbl 0658.58028
Let f: \(M\to M\) be a pseudo-Anosov diffeomorphism of an oriented compact surface M. It follows by a theorem of J. Franks [Proc. Symp. Pure Math. 14, 61-93 (1970; Zbl 0207.543)] that if the action induced by f on the first homology group is hyperbolic, then there is a compact invariant set for the toral automorphism associated with this action. It is shown in the paper under review that if the stable and unstable foliations of f are orientable, then the invariant set is a finite union of topological 2-discs. Applying some ideas of M. Urbanski [Stud. Math. 81, 37-51 (1985; Zbl 0625.58020)] the author proves that the lower capacity of the related invariant set is greater than 2.
Reviewer: L.N.Stoyanov

MSC:
37D99 Dynamical systems with hyperbolic behavior
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
57R30 Foliations in differential topology; geometric theory
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