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This article is cited in 4 scientific papers (total in 4 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.
Received: January 10, 2003
Citation:
Yu. S. Ilyashenko, V. S. Moldavskii, “Morse–Smale circle diffeomorphisms and moduli of elliptic curves”, Mosc. Math. J., 3:2 (2003), 531–540
Linking options:
https://www.mathnet.ru/eng/mmj98 https://www.mathnet.ru/eng/mmj/v3/i2/p531
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