On orbits of endomorphisms of tori and the schmidt game

Dani, S. G. (1988) On orbits of endomorphisms of tori and the schmidt game Ergodic Theory & Dynamical Systems, 8 (4). pp. 523-529. ISSN 0143-3857

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S0143385700004673

Abstract

We show that there exists a subset F of the n-dimensional torus Tn such that F has Hausdorff dimension n and for any xε F and any semisimple automorphism σ of Tn the closure of the σ -orbit of x contains no periodic points.

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