Polynomial 3-mixing for smooth time-changes of horocycle flows

Adam Kanigowski, Davide Ravotti

Research output: Contribution to journalArticleResearchpeer-review


Let (ht)t∈ℝbe the horocycle ow acting on (M, μ) = (Γ\ SL(2, ℝ); μ), where Γ is a co-compact lattice in SL(2, ℝ) and μ is the homogeneous probability measure locally given by the Haar measure on SL(2, ℝ). Let τ ∈ W6(M) be a strictly positive function and let μτbe the measure equivalent to μ with density τ. We consider the time changed ow (hτt)t∈ℝand we show that there exists γ=γ (M, τ) > 0 and a constant C > 0 such that for any f0, f1, f2∈ W6(M) and for all 0 = t0< t1< t2, we have (Equation Presented). With the same techniques, we establish polynomial mixing of all orders under the additional assumption of τ being fully supported on the discrete series.

Original languageEnglish
Pages (from-to)5347-5371
Number of pages25
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number9
Publication statusPublished - Sep 2020


  • Horocycle ow
  • Multiple mixing
  • Polynomial mixing
  • Shearing
  • Smooth time-changes

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