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Israel Journal of Mathematics

, Volume 122, Issue 1, pp 29–42 | Cite as

p-adic foliation and equidistribution

  • Elon Lindenstrauss
Article

Abstract

We show that if μ is a measure on ℝ/ℤ ergodic under the ×m map with positive entropy, then μ-a.s. {a n x} is equidistributed, for a significantly larger collection of integer sequencesa n than was previously known. In particular, we show that μ-a.s. {r n x} is equidistributed as long asm does not divide any power ofr (this was previously known only ifr andm are relatively prime). The proof uses thep-adic analogue of results from the theory of smooth dynamical systems.

Keywords

Lyapunov Exponent Invariant Measure Ergodic Theory Hausdorff Dimension Ergodic Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 2001

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.Department of MathematicsStanford UniversityStanfordUSA

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