On the number of zeros of Abelian integrals
- Gal BinyaminiAffiliated withWeizmann Institute of Science
- , Dmitry NovikovAffiliated withWeizmann Institute of Science
- , Sergei YakovenkoAffiliated withWeizmann Institute of Science Email author
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We prove that the number of limit cycles generated from nonsingular energy level ovals (periodic trajectories) in a small non-conservative perturbation of a Hamiltonian polynomial vector field on the plane, is bounded by a double exponential of the degree of the fields. This solves the long-standing infinitesimal Hilbert 16th problem.
The proof uses only the fact that Abelian integrals of a given degree are horizontal sections of a regular flat meromorphic connection defined over ℚ (the Gauss-Manin connection) with a quasiunipotent monodromy group.
Mathematics Subject Classification (2000)34C07 34C08 34M10 34M60 14Q20 32S40
- On the number of zeros of Abelian integrals
Volume 181, Issue 2 , pp 227-289
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