Simultaneous dense and nondense orbits for commuting maps

V Bergelson; M Einsiedler; Jimmy Tseng

doi:10.1007/s11856-015-1244-y

Simultaneous dense and nondense orbits for commuting maps

V Bergelson, M Einsiedler, Jimmy Tseng

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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.

Original language	English
Pages (from-to)	23-45
Number of pages	23
Journal	Israel Journal of Mathematics
Volume	210
Issue number	1
Early online date	3 Nov 2015
DOIs	https://doi.org/10.1007/s11856-015-1244-y
Publication status	Published - 2015

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The final publication is available at Springer via http://dx.doi.org/10.1007/s11856-015-1244-y
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title = "Simultaneous dense and nondense orbits for commuting maps",

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.",

author = "V Bergelson and M Einsiedler and Jimmy Tseng",

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AU - Bergelson, V

AU - Einsiedler, M

AU - Tseng, Jimmy

PY - 2015

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AB - 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.

U2 - 10.1007/s11856-015-1244-y

DO - 10.1007/s11856-015-1244-y

M3 - Article (Academic Journal)

SN - 0021-2172

VL - 210

SP - 23

EP - 45

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

Simultaneous dense and nondense orbits for commuting maps

Abstract

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