Orbits of certain endomorphisms of nilmanifolds and Hausdorff dimension
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 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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