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Dulac's theorem
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(Theorem)
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Let
 be an analytic planar system, then in any bounded region of the plane there is at most a finite number of limit cycles. Also any polynomial planar system has at most a finite number of limit cycles.[PL]
note about the proof: The proof was given by Dulac in 1923, but an error was found in the proof. In 1988 Jean Ecalle, Jacques Martinet, Robert Moussu, Jean Pierre Ramis and independently Yulij Ilyashenko corrected the error in the proof.[PL]
- PL
- Perko, Lawrence: Differential Equations and Dynamical Systems. Springer-Verlag, New York, 1991.
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"Dulac's theorem" is owned by Daume.
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(view preamble)
Cross-references: proof, polynomial, limit cycles, number, finite, plane, region, bounded, analytic
There are 2 references to this entry.
This is version 3 of Dulac's theorem, born on 2004-06-17, modified 2004-06-18.
Object id is 5930, canonical name is DulacsTheorem.
Accessed 2190 times total.
Classification:
| AMS MSC: | 34C07 (Ordinary differential equations :: Qualitative theory :: Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramif) |
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Pending Errata and Addenda
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