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 Trudy Mat. Inst. Steklova, 2007, Volume 256, Pages 252–266 (Mi tm465)

Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces

A. V. Kochergin

M. V. Lomonosov Moscow State University, Faculty of Economics

Abstract: A detailed proof of the absence of mixing is presented for a special flow constructed by an arbitrary rotation of the circle and by a symmetric function with logarithmic singularities (i.e., a function for which the sums of the coefficients of logarithms for “right” and “left” singularities are equal).

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English version:
Proceedings of the Steklov Institute of Mathematics, 2007, 256, 238–252

Bibliographic databases:

UDC: 517.9
Received in July 2006

Citation: A. V. Kochergin, “Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Trudy Mat. Inst. Steklova, 256, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 252–266; Proc. Steklov Inst. Math., 256 (2007), 238–252

Citation in format AMSBIB
\Bibitem{Koc07} \by A.~V.~Kochergin \paper Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces \inbook Dynamical systems and optimization \bookinfo Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov \serial Trudy Mat. Inst. Steklova \yr 2007 \vol 256 \pages 252--266 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm465} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2336903} \zmath{https://zbmath.org/?q=an:1153.37303} \elib{https://elibrary.ru/item.asp?id=9482618} \transl \jour Proc. Steklov Inst. Math. \yr 2007 \vol 256 \pages 238--252 \crossref{https://doi.org/10.1134/S0081543807010130} \elib{https://elibrary.ru/item.asp?id=13560203} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248333083} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Ulcigrai C., “Slow Chaos in Surface Flows”, Boll. Unione Mat. Ital.
2. Chaika J., Fraczek K., Kanigowski A., Ulcigrai C., “Singularity of the Spectrum For Smooth Area-Preserving Flows in Genus Two and Translation Surfaces Well Approximated By Cylinders”, Commun. Math. Phys.
3. Ulcigrai C., “Weak mixing for logarithmic flows over interval exchange transformations”, J. Mod. Dyn., 3:1 (2009), 35–49
4. Scheglov D., “Absence of mixing for smooth flows on genus two surfaces”, J. Mod. Dyn., 3:1 (2009), 13–34
5. Ulcigrai C., “Absence of mixing in area-preserving flows on surfaces”, Ann. of Math. (2), 173:3 (2011), 1743–1778
6. Avila A., Forni G., Ulcigrai C., “Mixing for Time-Changes of Heisenberg Nilflows”, J. Differential Geom., 89:3 (2011), 369–410
7. Knill O., Tangerman F., “Self-similarity and growth in Birkhoff sums for the golden rotation”, Nonlinearity, 24:11 (2011), 3115–3127
8. A. I. Bufetov, B. M. Gurevich, K. M. Khanin, F. Cellarosi, “The Abel Prize award to Ya. G. Sinai”, Russian Math. Surveys, 69:5 (2014), 931–956
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