Equidistribution of singular measures on nilmanifolds and skew products

  title={Equidistribution of singular measures on nilmanifolds and skew products},
  author={Fabrizio Polo},
  journal={Ergodic Theory and Dynamical Systems},
  pages={1785 - 1817}
  • F. Polo
  • Published 16 March 2010
  • Mathematics
  • Ergodic Theory and Dynamical Systems
Abstract We prove that for a minimal rotation T on a two-step nilmanifold and any measure μ, the push-forward Tn⋆μ of μ under Tn tends toward Haar measure if and only if μ projects to Haar measure on the maximal torus factor. For an arbitrary nilmanifold we get the same result along a sequence of uniform density one. These results strengthen Parry’s result [Ergodic properties of affine transformations and flows on nilmanifolds. Amer. J. Math.91 (1968), 757–771] that such systems are uniquely… 
Closed Ideals in the Stone-Cech Compactification of a Countable Semigroup and Some Applications to Ergodic Theory and Topological Dynamics
We study the relationship between algebra in the Stone-Čech compactification βS of a countable semigroup and dynamics. In particular, we establish a correspondence between the closed subsets of βS
ETS volume 31 issue 6 Cover and Back matter
  • Ergodic Theory and Dynamical Systems
  • 2011


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