Page 1

Displaying 1 – 4 of 4

Showing per page

On the number of limit cycles of a generalized Abel equation

Naeem Alkoumi, Pedro J. Torres (2011)

Czechoslovak Mathematical Journal

New results are proved on the maximum number of isolated T -periodic solutions (limit cycles) of a first order polynomial differential equation with periodic coefficients. The exponents of the polynomial may be negative. The results are compared with the available literature and applied to a class of polynomial systems on the cylinder.

On the number of zeros of Melnikov functions

Sergey Benditkis, Dmitry Novikov (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We provide an effective uniform upper bound for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field. The bound depends on degrees of the field and of the perturbation, and on the order k of the Melnikov function. The generic case k = 1 was considered by Binyamini, Novikov and Yakovenko [BNY10]. The bound follows from an effective construction of the Gauss-Manin connection for iterated integrals.

Currently displaying 1 – 4 of 4

Page 1