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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Volume 254, Pages 162–180 (Mi tm106)  
This article is cited in 5 scientific papers (total in 5 papers)

Topology of Analytic Foliations in C2. The Kupka–Smale Property

T. S. Firsova

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (289 kB) Citations (5)
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Abstract: The topology of leaves of a generic analytic foliation on the complex plane is studied. It is proved that for a generic foliation all leaves are topological disks except for at most a countable number of topological cylinders. It is also shown that such foliations possess the Kupka–Smale property.
Received in October 2005
English version:
Proceedings of the Steklov Institute of Mathematics, 2006, Volume 254, Pages 152–168
DOI: https://doi.org/10.1134/S0081543806030060
Bibliographic databases:
UDC: 517.927.7
Language: Russian
Citation: T. S. Firsova, “Topology of Analytic Foliations in C2. The Kupka–Smale Property”, Nonlinear analytic differential equations, Collected papers, Trudy Mat. Inst. Steklova, 254, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 162–180; Proc. Steklov Inst. Math., 254 (2006), 152–168
Citation in format AMSBIB
\Bibitem{Fir06}
\by T.~S.~Firsova
\paper Topology of Analytic Foliations in~$\mathbb C^2$. The Kupka--Smale Property
\inbook Nonlinear analytic differential equations
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2006
\vol 254
\pages 162--180
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm106}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2301003}
\zmath{https://zbmath.org/?q=an:1351.37198}
\elib{https://elibrary.ru/item.asp?id=13510448}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 254
\pages 152--168
\crossref{https://doi.org/10.1134/S0081543806030060}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33749373848}
Linking options:
  • https://www.mathnet.ru/eng/tm106
  • https://www.mathnet.ru/eng/tm/v254/p162
    • This publication is cited in the following 5 articles:
    1. Goncharuk N., Kudryashov Yu., “Cheap Complex Limit Cycles”, Nonlinearity, 31:3 (2018), 909–919  crossref  mathscinet  zmath  isi  scopus
    2. Nataliya Goncharuk, Yury Kudryashov, “Genera of non-algebraic leaves of polynomial foliations of C2”, Mosc. Math. J., 18:1 (2018), 63–83  mathnet  crossref
    3. Golenishcheva-Kutuzova T., Kleptsyn V., “Minimality and ergodicity of a generic analytic foliation of C2”, Ergodic Theory Dynam. Systems, 28:5 (2008), 1533–1544  crossref  mathscinet  zmath  isi  elib  scopus
    4. Ilyashenko Yu., “Some open problems in real and complex dynamical systems”, Nonlinearity, 21:7 (2008), T101–T107  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. T. I. Golenishcheva-Kutuzova, “A Generic Analytic Foliation in C2 Has Infinitely Many Cylindrical Leaves”, Proc. Steklov Inst. Math., 254 (2006), 180–183  mathnet  crossref  mathscinet  zmath
    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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