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SUMMARY:Simultaneous dense and nondense orbits for commuting maps - Tseng\
 , J (University of Bristol)
DTSTART:20140611T103000Z
DTEND:20140611T113000Z
UID:TALK52940@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We show that\, for two commuting automorphisms of the d-torus\
 , many points have drastically different orbit structures for the two maps
 . Specifically\, using measure rigidity\, the Ledrappier-Young formula\, a
 nd the Marstrand slicing theorem\, we show that the set of points that hav
 e dense orbit under one map and nondense orbit under the other has full Ha
 usdorff dimension. This mixed case\, dense orbit under one map and nondens
 e orbit under the other\, is much more delicate than the other two possibl
 e cases. Our technique can also be applied to other settings. For example\
 , we show the analogous result for two elements of the Cartan action on co
 mpact higher rank homogeneous spaces. This is joint work with V. Bergelson
  and M. Einsiedler.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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