Detecting alien limit cycles near a Hamiltonian 2-saddle cycle

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LUCA, Stijn; DUMORTIER, Freddy; Caubergh, M.; Roussarie, R.;
  • Publisher: Dept. of Mathematics, Southwest Missouri State University
  • Related identifiers: doi: 10.3934/dcds.2009.25.1081
  • Subject: limit cycle | alien limit cycle | Planar vector field | Hamiltonian perturbation | Planar vector field; Hamiltonian perturbation; limit cycle; Abelian integral; two-saddle cycle; alien limit cycle; transition map | Abelian integral | two-saddle cycle | transition map

This paper aims at providing an example of a cubic Hamiltonian 2-saddle cycle that after bifurcation can give rise to an alien limit cycle; this is a limit cycle that is not controlled by a zero of the related Abelian integral. To guarantee the existence of an alien lim... View more
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