RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mosc. Math. J.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mosc. Math. J., 2003, Volume 3, Number 2, Pages 531–540 (Mi mmj98)  

This article is cited in 3 scientific papers (total in 3 papers)

Morse–Smale circle diffeomorphisms and moduli of elliptic curves

Yu. S. Ilyashenkoab, V. S. Moldavskiib

a Steklov Mathematical Institute, Russian Academy of Sciences
b Cornell University

Abstract: To any circle diffeomorphism there corresponds, by a classical construction of V. I. Arnold, a one-parameter family of elliptic curves. Arnold conjectured that, as the parameter approaches zero, the modulus of the corresponding elliptic curve tends to the (Diophantine) rotation number of the original diffeomorphism. In this paper, we disprove the generalization of this conjecture to the case when the diffeomorphism in question is Morse–Smale. The proof relies on the theory of quasiconformal mappings.

Key words and phrases: Circle diffeomorphism, rotation number, moduli of elliptic curves, quasiconformal mappings.

DOI: https://doi.org/10.17323/1609-4514-2003-3-2-531-540

Full text: http://www.ams.org/.../abst3-2-2003.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 37E10, 37F30
Received: January 10, 2003
Language:

Citation: Yu. S. Ilyashenko, V. S. Moldavskii, “Morse–Smale circle diffeomorphisms and moduli of elliptic curves”, Mosc. Math. J., 3:2 (2003), 531–540

Citation in format AMSBIB
\Bibitem{IlyMol03}
\by Yu.~S.~Ilyashenko, V.~S.~Moldavskii
\paper Morse--Smale circle diffeomorphisms and moduli of elliptic curves
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 2
\pages 531--540
\mathnet{http://mi.mathnet.ru/mmj98}
\crossref{https://doi.org/10.17323/1609-4514-2003-3-2-531-540}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2025272}
\zmath{https://zbmath.org/?q=an:1040.37026}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208594200011}
\elib{http://elibrary.ru/item.asp?id=8379113}


Linking options:
  • http://mi.mathnet.ru/eng/mmj98
  • http://mi.mathnet.ru/eng/mmj/v3/i2/p531

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. N. B. Goncharuk, “Rotation Numbers and Moduli of Elliptic Curves”, Funct. Anal. Appl., 46:1 (2012), 11–25  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Buff X., Goncharuk N., “Complex Rotation Numbers”, J. Mod. Dyn., 9 (2015), 169–190  crossref  mathscinet  zmath  isi  elib
    3. Goncharuk N., “Complex Rotation Numbers: Bubbles and Their Intersections”, Anal. PDE, 11:7 (2018), 1787–1801  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
    Number of views:
    This page:231
    References:44

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020