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.
|Number of pages||25|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - Sep 2020|
- Horocycle ow
- Multiple mixing
- Polynomial mixing
- Smooth time-changes