a1 Department of Mathematics, University of Wales, Aberystwyth, Dyfed, Wales SY23 3BZ, U.K.
Conditions for the existence of a centre in two-dimensional systems are considered along the lines of Darboux. We show how these methods can be used in the search for maximal numbers of bifurcating limit cycles. We also extend the method to include more degenerate cases such as are encountered in less generic systems. These lead to new classes of integrals. In particular, the Kukles system is considered, and new centre conditions for this system are obtained.
(Received June 26 1991)
(Revised August 27 1993)
p1 Present address: Department of Mathematics, Bogazici University, 80815 Bebek, Istanbul, Turkey.