Polynomial decay of correlations for a class of smooth flows on the two torus

Bassam Fayad

Bulletin de la Société Mathématique de France (2001)

  • Volume: 129, Issue: 4, page 487-503
  • ISSN: 0037-9484

Abstract

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Kočergin introduced in 1975 a class of smooth flows on the two torus that are mixing. When these flows have one fixed point, they can be viewed as special flows over an irrational rotation of the circle, with a ceiling function having a power-like singularity. Under a Diophantine condition on the rotation’s angle, we prove that the special flows actually have a t - η -speed of mixing, for some η > 0 .

How to cite

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Fayad, Bassam. "Polynomial decay of correlations for a class of smooth flows on the two torus." Bulletin de la Société Mathématique de France 129.4 (2001): 487-503. <http://eudml.org/doc/272405>.

@article{Fayad2001,
abstract = {Kočergin introduced in 1975 a class of smooth flows on the two torus that are mixing. When these flows have one fixed point, they can be viewed as special flows over an irrational rotation of the circle, with a ceiling function having a power-like singularity. Under a Diophantine condition on the rotation’s angle, we prove that the special flows actually have a $t^\{-\eta \}$-speed of mixing, for some $\eta &gt;0$.},
author = {Fayad, Bassam},
journal = {Bulletin de la Société Mathématique de France},
keywords = {flows on the torus; special flows; speed of mixing; correlations},
language = {eng},
number = {4},
pages = {487-503},
publisher = {Société mathématique de France},
title = {Polynomial decay of correlations for a class of smooth flows on the two torus},
url = {http://eudml.org/doc/272405},
volume = {129},
year = {2001},
}

TY - JOUR
AU - Fayad, Bassam
TI - Polynomial decay of correlations for a class of smooth flows on the two torus
JO - Bulletin de la Société Mathématique de France
PY - 2001
PB - Société mathématique de France
VL - 129
IS - 4
SP - 487
EP - 503
AB - Kočergin introduced in 1975 a class of smooth flows on the two torus that are mixing. When these flows have one fixed point, they can be viewed as special flows over an irrational rotation of the circle, with a ceiling function having a power-like singularity. Under a Diophantine condition on the rotation’s angle, we prove that the special flows actually have a $t^{-\eta }$-speed of mixing, for some $\eta &gt;0$.
LA - eng
KW - flows on the torus; special flows; speed of mixing; correlations
UR - http://eudml.org/doc/272405
ER -

References

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  1. [1] B. Fayad – « Analytic mixing reparametrizations for irrational flows on the torus 𝕋 n , n ≥ 3 », to appear in Ergodic Theory and Dynamical Flows. Zbl1136.37307
  2. [2] —, « Weak mixing for reparametrized linear flows on the torus », to appear in Ergodic Theory and Dynamical Flows. 
  3. [3] K. Khanin & Y. Sinai – « Mixing of some classes of special flows over rotations of the circle », Funkts. Anal. Prilozhen.26 (1992), p. 155–169. Zbl0797.58045MR1189019
  4. [4] A. Kočergin – « Mixing in special flows over a rearrangment of segments and in smooth flows on surfaces », Mat. USSR Sbornik25 (1975), p. 471–502. Zbl0326.28030MR516507
  5. [5] —, « Nonsingular saddle points and absence of mixing », Math. Zametki19 (1976), p. 453–468. Zbl0344.28008MR415681
  6. [6] M. Shklover – « On dynamical systems on the torus with continuous spectrum », Izv. Vuzov10 (1967), p. 113–124. Zbl0153.12602MR226147

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