Orbits of certain endomorphisms of nilmanifolds and Hausdorff dimension

Details Orbits of certain endomorphisms of nilmanifolds and Hausdorff dimension Orbits of certain endomorphisms of nilmanifolds and Hausdorff dimension

2002-12-09

arxiv.org/abs/math/0212118v1

Mathematics

Differential Geometry

11 pages

Scientific paper

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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