October 1998
Journal of the London Mathematical Society;10/01/1998, Vol. 58 Issue 2, p353
Academic Journal
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)=½y2-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.


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