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Simultaneous bifurcation of limit cycles from two nests of periodic orbits |
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| Authors: | Antonio Garijo |
| Institution: | a Departament d'Eng. Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans, 26, 43007 Tarragona, Spain b Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain c Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain |
| Abstract: | Let  be an holomorphic differential equation having a center at p, and consider the following perturbation  . We give an integral expression, similar to an Abelian integral, whose zeroes control the limit cycles that bifurcate from the periodic orbits of the period annulus of p. This expression is given in terms of the linearizing map of  at p. The result is applied to control the simultaneous bifurcation of limit cycles from the two period annuli of  , after a polynomial perturbation. |
| Keywords: | Holomorphic vector fields Bifurcation Limit cycle |
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