We study quadratic perturbations of the integrable system (1 + x)dH, where H = (x2 + y2)/2. We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

We consider a planar differential system ˙ x = P (x, y), ˙ y = Q(x, y), where P and Q are C 1 functions in some open set U ⊆ R 2 , and ˙ = d dt. Let γ be a periodic orbit of the system in U. Let f (x, y) : U ⊆ R 2 → R be a C 1 function such that P (x, y) ∂f ∂x (x, y) + Q(x, y) ∂f ∂y (x, y) = k(x, y) f (x, y), where k(x, y) is a C 1 function in U and γ ⊆ {(x, y) | f (x, y) = 0}. We assume that i...

39 We shall give three ' criteria for the uniqueness of limit cycles of systems of Liellard type x '= a(y)-f3(y)F(x}, y '= -g(x}, examples are provided to illustrate our results.

Motivated by the recent work of Louko and Molgado, we consider the Ashtekar-Horowitz-Boulware model using the projection operator formalism. This paper uses the techniques developed in a recent paper of Klauder and Little to overcome the potential difficulties of this particular model. We also extend the model by including a larger class of functions than previously considered and evaluate the ...

OBJECTIVES To determine individual differences in the impact of illness on the change in performance of swimmers in international competitions. METHODS Subjects were members of the Australian swimming team (33 male and 39 female, aged 15-27 years). Swimmers provided a weekly seven day recall of symptoms of illness during final six weeks of preparations for international competition over a thr...

We investigate the possibility that the large mixing of neutrinos is induced by their large coupling to a five-dimensional bulk neutrino. In the strong coupling limit the model is exactly soluble. It gives rise to an oscillation amplitude whose squared-mass difference is independent of the channel, thus making it impossible to explain both the solar and the atmospheric neutrino oscillations sim...