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Well-approximable angles and mixing for flows on $\mathbb{T} ^2$ with nonsingular fixed points

Author(s): A. Kochergin
Journal: Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 113-121.
MSC (2000): Primary 37E35, 37A25
Posted: October 26, 2004
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Abstract: We consider special flows over circle rotations with an asymmetric function having logarithmic singularities. If some expressions containing singularity coefficients are different from any negative integer, then there exists a class of well-approximable angles of rotation such that the special flow over the rotation of this class is mixing.

References:

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V. I. Arnold, Topological and ergodic properties of closed 1-forms with incommesurable periods, Funkts. Anal. i Prilozh. 25 (1991), no. 2, 1-12; English transl., Funct. Anal. Appl. 25 (1991), no. 2, 81-90. MR 1142204 (93e:58104)

2.
K. M. Khanin and Ya. G. Sinai, A mixing for some classes of special flows over rotations of the circle, Funkts. Anal. i Prilozh. 26 (1992), no. 3, 1-21; English transl., Funct. Anal. Appl. 26 (1992), no. 3, 155-169. MR 1189019 (93j:58079)

3.
A. V. Kochergin, Nonsingular saddle points and the absence of mixing, Math. Notes 19 (1976), 277-287. MR 415681 (54:3761)

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A. V. Kochergin, Nonsingular saddle points and mixing in flows on two-dimensional torus, Sb. Math. 194 (2003), no. 7-8, 1195-1224. MR 2034533

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A. V. Kochergin, Nonsingular saddle points and mixing in flows on two-dimensional torus II, Mat. Sb. 195 (2004), no. 3, 15-46. (Russian) MR 2068956

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Additional Information:

A. Kochergin
Affiliation: Department of Economics, Lomonosov Moscow State University, Leninskie Gory, Moscow 119992, Russia
Email: avk@econ.msu.ru

DOI: 10.1090/S1079-6762-04-00136-2
PII: S 1079-6762(04)00136-2
Received by editor(s): June 14, 2004
Posted: October 26, 2004
Additional Notes: The work was partially supported by the program ``Leading Scientific Schools of Russian Federation", project no. NSh-457.2003.01.
Dedicated: To the Anniversary of Anatole Katok, my Friend and Teacher.
Communicated by: Svetlana Katok
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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