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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 256, Pages 252–266 (Mi tm465)  
This article is cited in 11 scientific papers (total in 12 papers)

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

A. V. Kochergin

M. V. Lomonosov Moscow State University, Faculty of Economics
Full-text PDF (221 kB) Citations (12)
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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).
Received in July 2006
English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 256, Pages 238–252
DOI: https://doi.org/10.1134/S0081543807010130
Bibliographic databases:
UDC: 517.9
Language: Russian
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
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\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.
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 256
\pages 238--252
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Linking options:
  • https://www.mathnet.ru/eng/tm465
  • https://www.mathnet.ru/eng/tm/v256/p252
    • This publication is cited in the following 12 articles:
    1. Mariusz Lemańczyk, “Ergodicity, mixing, Ratner's properties and disjointness for classical flows: On the research of Corinna Ulcigrai”, JMD, 18 (2022), 103  crossref
    2. Ulcigrai C., “Slow Chaos in Surface Flows”, Boll. Unione Mat. Ital., 14:1 (2021), 231–255  crossref  mathscinet  isi  scopus
    3. 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., 381:3 (2021), 1369–1407  crossref  mathscinet  isi
    4. Bassam Fayad, Giovanni Forni, Adam Kanigowski, “Lebesgue spectrum of countable multiplicity for conservative flows on the torus”, J. Amer. Math. Soc., 34:3 (2021), 747  crossref
    5. Artur Avila, Giovanni Forni, Davide Ravotti, Corinna Ulcigrai, “Mixing for smooth time-changes of general nilflows”, Advances in Mathematics, 385 (2021), 107759  crossref
    6. F. Cellarosi, The Abel Prize, The Abel Prize 2013-2017, 2019, 207  crossref
    7. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Ulcigrai C., “Absence of mixing in area-preserving flows on surfaces”, Ann. of Math. (2), 173:3 (2011), 1743–1778  crossref  mathscinet  zmath  isi  scopus
    9. Avila A., Forni G., Ulcigrai C., “Mixing for Time-Changes of Heisenberg Nilflows”, J. Differential Geom., 89:3 (2011), 369–410  crossref  mathscinet  zmath  isi  elib  scopus
    10. Knill O., Tangerman F., “Self-similarity and growth in Birkhoff sums for the golden rotation”, Nonlinearity, 24:11 (2011), 3115–3127  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Ulcigrai C., “Weak mixing for logarithmic flows over interval exchange transformations”, J. Mod. Dyn., 3:1 (2009), 35–49  crossref  mathscinet  zmath  isi  elib  scopus
    12. Scheglov D., “Absence of mixing for smooth flows on genus two surfaces”, J. Mod. Dyn., 3:1 (2009), 13–34  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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