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A non-mixing Arnold flow on a surface.(English)Zbl 07989619

Summary: We construct a smooth area preserving flow on a genus 2 surface with exactly one open uniquely ergodic component, that is asymmetrically bounded by separatrices of non-degenerate saddles and that is nevertheless not mixing.

MSC:

37E35 Flows on surfaces
37A25 Ergodicity, mixing, rates of mixing

Cite

References:

[1]Arnol’d, V., Topological and ergodic properties of closed 1-forms with incommensurable periods, Funkc. Anal. Prilozh.. Funkc. Anal. Prilozh., Funct. Anal. Appl., 25, 2, 81-90, 1991, Translated in: ·Zbl 0732.58001
[2]Chaika, J.; Wright, A., A smooth mixing flow on a surface with non-degenerate fixed points, J. Am. Math. Soc., 32, 81-117, 2019 ·Zbl 1454.37025
[3]Conze, J-P.; Fraczek, K., Cocycles over interval exchange transformations and multivalued Hamiltonian flows, Adv. Math., 226, 5, 4373-4428, 2011 ·Zbl 1236.37006
[4]Dolgopyat, D.; Fayad, B., Limit Theorems for Toral Translations, Proceedings of Symposia in Pure Mathematics, vol. 89, 2015 ·Zbl 1375.37014
[5]Fayad, B., Polynomial decay of correlations for a class of smooth flows on the two torus, Bull. Soc. Math. Fr., 129, 487-503, 2001 ·Zbl 1187.37009
[6]Fayad, B.; Kanigowski, A., On multiple mixing for a class of conservative surface flows, Invent. Math., 203, 2, 555-614, 2016 ·Zbl 1358.37018
[7]Fayad, B.; Forni, G.; Kanigowski, A., Lebesgue spectrum of countable multiplicity for conservative flows on the torus, J. Am. Math. Soc., 34, 2021 ·Zbl 1493.37008
[8]Forni, G., Deviation of ergodic averages for area-preserving flows on surfaces of higher genus, Ann. Math., 155, 1, 1-103, 2002 ·Zbl 1034.37003
[9]Katok, A., Invariant measures of flows on orientable surfaces, Dokl. Akad. Nauk SSSR, 211, 775-778, 1973, (in Russian)
[10]Kochergin, A., Nonsingular saddle points and the absence of mixing, Mat. Zametki, 19, 3, 453-468, 1976, Translated in: Math. Notes 19 (3) 277-286 ·Zbl 0344.28008
[11]Khanin, K. M.; Sinai, Ya. G., Mixing for some classes of special flows over rotations of the circle, Funkc. Anal. Prilozh.. Funkc. Anal. Prilozh., Funct. Anal. Appl., 26, 3, 155-169, 1992, Translated in: ·Zbl 0797.58045
[12]Kochergin, A. V., Mixing in special flows over a shifting of segments and in smooth flows on surfaces, Mat. Sb. (N.S.), 96, 138, 471-502, 1975 ·Zbl 0321.28012
[13]Kochergin, A. V., Nondegenerate fixed points and mixing in flows on a two-dimensional torus I, Sb. Math.. Sb. Math., Sb. Math., 195, 317-346, 2004, II: ·Zbl 1077.37006
[14]Kochergin, A. V., Causes of stretching of Birkhoff sums and mixing in flows on surfaces, (Basselblatt, B., Dynamics, Ergodic Theory and Geometry, 2010, Cambridge University Press)
[15]Kochergin, A., Well-approximable angles and mixing for flows on \(\mathbb{T}^2\) with nonsingular fixed points, Electron. Res. Announc. Am. Math. Soc., 10, 113-121, October 26, 2004 ·Zbl 1068.37027
[16]Levitt, G., Feuillettages des surfaces, 1983, thèse
[17]Mayer, A., Trajectories on the closed orientable surfaces, Rec. Math. [Mat. Sb.] N.S., 12, 54, 71-84, 1943 ·Zbl 0063.03856
[18]Novikov, S. P., The Hamiltonian formalism and a multivalued analogue of Morse theory, Usp. Mat. Nauk, 37, 5(227), 3-49, 1982 ·Zbl 0571.58011
[19]Novikov, S. P., The semiclassical electron in a magnetic field and lattice. Some problems of low dimensional “periodic” topology, Geom. Funct. Anal. (GAFA), 5, 2, 434-444, 1995 ·Zbl 0853.57014
[20]Ravotti, D., Quantitative mixing for locally Hamiltonian flows with saddle loops on compact surfaces, Ann. Henri Poincaré, 18, 12, 3815-3861, 2017 ·Zbl 1417.37189
[21]Sataev, A., The number of invariant measures for flows on orientable surfaces, Izv. Akad. Nauk SSSR, Ser. Mat., 39, 4, 860-878, 1975, (in Russian) ·Zbl 0323.28012
[22]Scheglov, D., Absence of mixing for smooth flows on genus two surfaces, J. Mod. Dyn., 3, 1, 13-34, 2009 ·Zbl 1183.37080
[23]Ulcigrai, C., Mixing of asymmetric logarithmic suspension flows over interval exchange transformations, Ergod. Theory Dyn. Syst., 27, 991-1035, 2007 ·Zbl 1135.37004
[24]Ulcigrai, C., Absence of mixing in area-preserving flows on surfaces, Ann. Math., 173, 1743-1778, 2011 ·Zbl 1251.37003
[25]Ulcigrai, C., Dynamics and arithmetics of higher genus surface flows, (Proceedings of the International Congress of Mathematicians 2022, July 2022)
[26]Veech, W. A., Strict ergodicity in zero dimensional dynamical systems and the Kronecker-Weyl theorem \(\operatorname{mod} 2\), Trans. Am. Math. Soc., 140, 1-33, 1969 ·Zbl 0201.05601
[27]Zorich, A., Deviation for interval exchange transformations, Ergod. Theory Dyn. Syst., 17, 6, 1477-1499, 1997 ·Zbl 0958.37002
[28]Zorich, A., How do the leaves of a closed 1-form wind around a surface?, (Pseudoperiodic Topology. Pseudoperiodic Topology, Amer. Math. Soc. Transl. Ser. 2, vol. 197, 1999, Amer. Math. Soc.: Amer. Math. Soc. Providence, RI), 135-178 ·Zbl 0976.37012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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