Simultaneous dense and nondense orbits for commuting maps
Dynamical Systems
2014-05-22 v2
Abstract
We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using measure rigidity, we show that the set of points that have dense orbit under one map and nondense orbit under the second has full Hausdorff dimension.
Cite
@article{arxiv.1309.4823,
title = {Simultaneous dense and nondense orbits for commuting maps},
author = {Vitaly Bergelson and Manfred Einsiedler and Jimmy Tseng},
journal= {arXiv preprint arXiv:1309.4823},
year = {2014}
}
Comments
17 pages. Very minor changes to the exposition. Three additional papers cited