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arXiv · math/0212118

Orbits of certain endomorphisms of nilmanifolds and Hausdorff dimension

C. S. Aravida·Parameswaran Sankaran
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Abstract

We prove that for certain endomorphisms of a nilmanifold N the set S of those points such that the closure of its (forward) orbit contains no periodic points is large in the sense that for any non-empty open set U, the set U\cap S is of full Hausdorff dimension. When the manifold N is a torus, this result is due to S.G.Dani.

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C. S. Aravida, Parameswaran Sankaran. 2002-12-09. Orbits of certain endomorphisms of nilmanifolds and Hausdorff dimension. https://arxiv.org/abs/math/0212118

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