Naslov
A generalization of Françoise's algorithm for calculating higher order Melnikov functions.

Autori
Jebrane, Ahmed ; Mardešić, Pavao ; Pelletier, Michèle

Izvornik
Bulletin des Sciences Mathématiques (0007-4497) 126 (2002), 9; 705-732

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Abelian integral; Melnikov function; Limit cycle; Fuchs system

Sažetak
In [J. Differential Equations 146 (2) (1998) 320–335], Françoise gives an algorithm for calculating the first nonvanishing Melnikov function Mℓ of a small polynomial perturbation of a Hamiltonian vector field and shows that Mℓ is given by an Abelian integral. This is done under the condition that vanishing of an Abelian integral of any polynomial form ω on the family of cycles implies that the form is algebraically relatively exact. We study here a simple example where Françoise's condition is not verified. We generalize Françoise's algorithm to this case and we show that Mℓ belongs to the module above the Abelian integrals. We also establish the linear differential system verified by these Melnikov functions Mℓ(t).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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