p-adic foliation and equidistribution

Elon Lindenstrauss*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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

Original languageAmerican English
Pages (from-to)29-42
Number of pages14
JournalIsrael Journal of Mathematics
StatePublished - 2001
Externally publishedYes


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