TY - JOUR

T1 - Simultaneous bifurcation of limit cycles from two nests of periodic orbits

AU - Gasull, Armengol

AU - Garijo, Antonio

AU - Jarque, Xavier

PY - 2008/5/15

Y1 - 2008/5/15

N2 - Let over(z, ̇) = f (z) be an holomorphic differential equation having a center at p, and consider the following perturbation over(z, ̇) = f (z) + ε R (z, over(z, ̄)). 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 over(z, ̇) = f (z) at p. The result is applied to control the simultaneous bifurcation of limit cycles from the two period annuli of over(z, ̇) = i z + z2, after a polynomial perturbation. © 2007 Elsevier Inc. All rights reserved.

AB - Let over(z, ̇) = f (z) be an holomorphic differential equation having a center at p, and consider the following perturbation over(z, ̇) = f (z) + ε R (z, over(z, ̄)). 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 over(z, ̇) = f (z) at p. The result is applied to control the simultaneous bifurcation of limit cycles from the two period annuli of over(z, ̇) = i z + z2, after a polynomial perturbation. © 2007 Elsevier Inc. All rights reserved.

KW - Bifurcation

KW - Holomorphic vector fields

KW - Limit cycle

U2 - https://doi.org/10.1016/j.jmaa.2007.09.076

DO - https://doi.org/10.1016/j.jmaa.2007.09.076

M3 - Article

VL - 341

SP - 813

EP - 824

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

ER -