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Well-approximable angles and mixing for flows on  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
MathSciNet review:
2119032
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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:
- 1.
- 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)
- 4.
- 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
- 5.
- 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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