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Morse – Smale Circle Diffeomorphisms and Moduli of Elliptic Curves
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ilyashenko, Yulij Sergeevich |
| Copyright Year | 2003 |
| 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. 2000 Math. Subj. Class. 37E10, 37F30. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ams.org/distribution/mmj/vol3-2-2003/ilyashenko-moldavskis.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Arnold Generalization (Psychology) Modulus of continuity Population Parameter Rotation number |
| Content Type | Text |
| Resource Type | Article |
