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

Bulletin de la Société Mathématique de France (2001)

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

## Access Full Article

top## Abstract

top## How to cite

topFayad, 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 $\eta >0$.},

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 $\eta >0$.

LA - eng

KW - flows on the torus; special flows; speed of mixing; correlations

UR - http://eudml.org/doc/272405

ER -

## References

top- [1] B. Fayad – « Analytic mixing reparametrizations for irrational flows on the torus ${\mathbb{T}}^{n}$, $n\ge 3$ », to appear in Ergodic Theory and Dynamical Flows. Zbl1136.37307
- [2] —, « Weak mixing for reparametrized linear flows on the torus », to appear in Ergodic Theory and Dynamical Flows.
- [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] 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] —, « Nonsingular saddle points and absence of mixing », Math. Zametki19 (1976), p. 453–468. Zbl0344.28008MR415681
- [6] M. Shklover – « On dynamical systems on the torus with continuous spectrum », Izv. Vuzov10 (1967), p. 113–124. Zbl0153.12602MR226147

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.