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Mat. Sb., 2004, Volume 195, Number 9, Pages 19–36 (Mi msb843)  

This article is cited in 8 scientific papers (total in 8 papers)

Generalizations of theorems on mixing flows with non-degenerate saddle points on a 2-torus

A. V. Kochergin

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

Abstract: A result on mixing in the special flow constructed from a rotation of a circle and an asymmetric function with logarithmic singularities is generalized to the case of Liouville rotation angles, provided that the coefficients of the singularities satisfy certain relations. It is also shown that the presence of strictly logarithmic symmetric singularities does not obstruct mixing in the case of a strongly asymmetric function.

DOI: https://doi.org/10.4213/sm843

Full text: PDF file (289 kB)
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English version:
Sbornik: Mathematics, 2004, 195:9, 1253–1270

Bibliographic databases:

UDC: 517.987.5+517.938
MSC: 37E35, 37A25
Received: 26.02.2004

Citation: A. V. Kochergin, “Generalizations of theorems on mixing flows with non-degenerate saddle points on a 2-torus”, Mat. Sb., 195:9 (2004), 19–36; Sb. Math., 195:9 (2004), 1253–1270

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Kochergin, “Nondegenerate Saddles and Nonmixing Transformations II”, Math. Notes, 81:1 (2007), 126–129  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. V. Kochergin, “Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces”, Proc. Steklov Inst. Math., 256 (2007), 238–252  mathnet  crossref  mathscinet  zmath  elib  elib
    3. Ulcigrai C., “Mixing of asymmetric logarithmic suspension flows over interval exchange transformations”, Ergodic Theory Dynam. Systems, 27:3 (2007), 991–1035  crossref  mathscinet  zmath  isi  elib
    4. Frączek K., Lemańczyk M., “On the self-similarity problem for ergodic flows”, Proc. Lond. Math. Soc. (3), 99:3 (2009), 658–696  crossref  mathscinet  zmath  isi  elib
    5. Ulcigrai C., “Weak mixing for logarithmic flows over interval exchange transformations”, J. Mod. Dyn., 3:1 (2009), 35–49  crossref  mathscinet  zmath  isi  elib
    6. Corinna Ulcigrai, “Absence of mixing in area-preserving flows on surfaces”, Ann. Math, 173:3 (2011), 1743  crossref  mathscinet  zmath  isi
    7. Ravotti D., “Quantitative Mixing For Locally Hamiltonian Flows With Saddle Loops on Compact Surfaces”, Ann. Henri Poincare, 18:12 (2017), 3815–3861  crossref  mathscinet  zmath  isi  scopus
    8. Chaika J., Wright A., “A Smooth Mixing Flow on a Surface With Nondegenerate Fixed Points”, J. Am. Math. Soc., 32:1 (2019), 81–117  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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