Well-approximable angles and mixing for flows on $\mathbb {T}^2$ with nonsingular fixed points
Author:
A. Kochergin
Journal:
Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 113-121
MSC (2000):
Primary 37E35, 37A25
DOI:
https://doi.org/10.1090/S1079-6762-04-00136-2
Published electronically:
October 26, 2004
MathSciNet review:
2119032
Full-text PDF Free Access
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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.
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A-E 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.
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K7-E A. V. Kochergin, Nonsingular saddle points and mixing in flows on two-dimensional torus, Sb. Math. 194 (2003), no. 7-8, 1195–1224.
K8-E A. V. Kochergin, Nonsingular saddle points and mixing in flows on two-dimensional torus II, Mat. Sb. 195 (2004), no. 3, 15–46. (Russian)
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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
Received by editor(s):
June 14, 2004
Published electronically:
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
Article copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
