Simultaneous dense and nondense orbits for commuting maps

2013/09/18 by Bergelson, Vitaly, Einsiedler, Manfred, Tseng, Jimmy · 1 citation
#37A05 #37D05 #37D35 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.4823

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.

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• Simultaneously bounded and dense orbits for commuting Cartan actions

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