Simultaneous dense and nondense orbits for commuting maps

V Bergelson, M Einsiedler, Jimmy Tseng

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)
236 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)23-45
Number of pages23
JournalIsrael Journal of Mathematics
Issue number1
Early online date3 Nov 2015
Publication statusPublished - 2015

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