Canard cycles in generic fast-slow systems on the torus
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I. V. Shchurov
Translated by: E. Khukhro - Trans. Moscow Math. Soc. 2010, 175-207
- DOI: https://doi.org/10.1090/S0077-1554-2010-00184-7
- Published electronically: December 21, 2010
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Abstract:
In generic fast-slow systems with a single parameter on the two-dimensional torus, for arbitrarily small values of this parameter there exist attracting canard cycles. This is a key distinction between the dynamics on the torus and the dynamics of similar systems on the plane. This has already been proved for systems with a convex slow curve. This paper looks at systems with a nonconvex slow curve. Upper and lower estimates for the number of canard cycles are obtained. An open set of systems having a preassigned number of attracting canard cycles is constructed.References
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Bibliographic Information
- I. V. Shchurov
- Affiliation: Moscow State University
- Email: ilya@schurov.com
- Published electronically: December 21, 2010
- Additional Notes: This research was partially supported by the Russian Foundation for Basic Research (grant no. 10-01-00739-a).
- © Copyright 2010 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2010, 175-207
- MSC (2010): Primary 34E17; Secondary 34E15, 37G15, 70K70
- DOI: https://doi.org/10.1090/S0077-1554-2010-00184-7
- MathSciNet review: 2760044