Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres

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Resumen

In this paper we consider the unfolding of saddle-node X=1xUa(x,y)(x(xμ−ε)∂x−Va(x)y∂y), parametrized by (ε,a) with ε≈0 and a in an open subset A of Rα, and we study the Dulac time T(s;ε,a) of one of its hyperbolic sectors. We prove (theorem 1.1) that the derivative ∂sT(s;ε,a) tends to −∞ as (s,ε)→(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.
Idioma originalInglés
Páginas (desde-hasta)104-114
Número de páginas11
PublicaciónProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volumen153
N.º1
DOI
EstadoPublicada - 1 dic 2021

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