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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 original | Anglès |
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Pàgines (de-a) | 104-114 |
Nombre de pàgines | 11 |
Revista | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
Volum | 153 |
Número | 1 |
DOIs | |
Estat de la publicació | Publicada - 1 de des. 2021 |
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Invariantes locales y globales en geometria
Solanes Farres, G. (PI), Balacheff , F. N. (Co-Investigador/a Principal), Rubio Nuñez, R. (Col.laborador/a), Gallego Gomez, E. (Investigador/a), Heusener, M. (Investigador/a), Marin Perez, D. (Investigador/a), Meersseman, L. (Investigador/a), Nicolau Reig, M. (Investigador/a), Porti Pique, J. (Investigador/a), Reventos Tarrida, A. (Investigador/a) & Mijares Verdú, S. (Col.laborador/a)
Ministerio de Ciencia e Innovación (MICINN)
1/01/19 → 30/09/22
Projecte: Projectes i Ajuts a la Recerca