Polynomial decay of correlations for a class of smooth flows on the two torus
[Décroissance polynomiale des corrélations pour une classe de flots lisses sur 𝕋 2 ]
Bulletin de la Société Mathématique de France, Tome 129 (2001) no. 4, pp. 487-503.

Kočergin a introduit en 1975 une classe de flots C sur le tore à deux dimensions qui sont mélangeants. Quand ces flots ont un seul point fixe, ils correspondent à des flots spéciaux au-dessus d’une rotation irrationnelle du cercle, dont la fonction de suspension présente une singularité en puissance fractionnaire. Sous une condition diophantienne sur l’angle de la rotation, on prouve que ces flots spéciaux ont une vitesse de mélange en t -η , pour un certain η>0.

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.

DOI : https://doi.org/10.24033/bsmf.2405
Classification : 37E35
Mots clés : flots sur le tore, flots spéciaux, vitesse de mélange, corrélations
@article{BSMF_2001__129_4_487_0,
     author = {Fayad, Bassam},
     title = {Polynomial decay of correlations for a class of smooth flows on the two torus},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {487--503},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {129},
     number = {4},
     year = {2001},
     doi = {10.24033/bsmf.2405},
     zbl = {1187.37009},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/bsmf.2405/}
}
Fayad, Bassam. Polynomial decay of correlations for a class of smooth flows on the two torus. Bulletin de la Société Mathématique de France, Tome 129 (2001) no. 4, pp. 487-503. doi : 10.24033/bsmf.2405. http://archive.numdam.org/articles/10.24033/bsmf.2405/

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