Polynomial decay of correlations for a class of smooth flows on the two torus
Bulletin de la Société Mathématique de France, Volume 129 (2001) no. 4, p. 487-503

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 $\eta >0$.

Kočergin a introduit en 1975 une classe de flots ${C}^{\infty }$ 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 ${t}^{-\eta }$, pour un certain $\eta >0$.

DOI : https://doi.org/10.24033/bsmf.2405
Classification:  37E35
Keywords: flows on the torus, special flows, speed of mixing, correlations
@article{BSMF_2001__129_4_487_0,
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},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {129},
number = {4},
year = {2001},
pages = {487-503},
doi = {10.24033/bsmf.2405},
zbl = {1187.37009},
language = {en},
url = {http://www.numdam.org/item/BSMF_2001__129_4_487_0}
}

Fayad, Bassam. Polynomial decay of correlations for a class of smooth flows on the two torus. Bulletin de la Société Mathématique de France, Volume 129 (2001) no. 4, pp. 487-503. doi : 10.24033/bsmf.2405. http://www.numdam.org/item/BSMF_2001__129_4_487_0/

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