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On Second Order Bifurcations of Limit Cycles
Author(s) -
Iliev I. D.
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006486
Subject(s) - mathematics , eigenvalues and eigenvectors , singularity , conjecture , mathematical analysis , perturbation (astronomy) , limit (mathematics) , hamiltonian (control theory) , hamiltonian system , elliptic function , bifurcation , limit cycle , mathematical physics , pure mathematics , physics , quantum mechanics , nonlinear system , mathematical optimization
The paper derives a formula for the second variation of the displacement function for polynomial perturbations of Hamiltonian systems with elliptic or hyperelliptic Hamiltonians H ( x , y )=½ y 2 − U ( x ) in terms of the coefficients of the perturbation. As an application, the conjecture stated by C. Chicone that a specific cubic system appearing in a deformation of singularity with two zero eigenvalues has at most two limit cycles is proved.