In this paper we consider the unfolding of saddle-node X = 1/xU(a)(x, y)(x(x(mu) - epsilon)partial derivative(x) - V-a(x)y partial derivative(y)), parametrized by (epsilon, a) with epsilon approximate to 0 and a in an open subset A of R-alpha, and we study the Dulac time T(s;epsilon, a) of one of its hyperbolic sectors. We prove (theorem 1.1) that the derivative partial derivative T-s(s;epsilon, a) tends to -infinity as (s, epsilon) -> (0(+), 0) uniformly on compact subsets of A. This result is addressed to study the bifurcation of critical periods in the Loud's family of quadratic centres. In this regard we show (theorem 1.2) that no bifurcation occurs from certain semi-hyperbolic polycycles.
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