Simultaneous dense and nondense orbits for commuting maps
Bergelson, V; Einsiedler, M; Tseng, J
Date: 1 September 2015
Journal
Israel Journal of Mathematics
Publisher
Springer Verlag for Hebrew University Magnes Press
Publisher DOI
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 ...
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.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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