Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres
In this paper we consider the unfolding of saddle-node parametrized by with and in an open subset of and we study the Dulac time of one of its hyperbolic sectors. We prove (theorem 1.1) that the derivative tends to as uniformly on compact subsets of This result is addressed to study the bifurcation...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2021 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/531298 |
| Acesso em linha: | http://hdl.handle.net/2072/531298 |
| Access Level: | Acceso aberto |
| Palavra-chave: | asymptotic expansions Dulac time Period function saddle-node unfolding 51 |
| Resumo: | In this paper we consider the unfolding of saddle-node parametrized by with and in an open subset of and we study the Dulac time of one of its hyperbolic sectors. We prove (theorem 1.1) that the derivative tends to as uniformly on compact subsets of 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. © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh. |
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