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...

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Detalles Bibliográficos
Autores: Marín, D., Saavedra, M., Villadelprat, J.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/531298
Acceso en línea:http://hdl.handle.net/2072/531298
Access Level:acceso abierto
Palabra clave:asymptotic expansions
Dulac time
Period function
saddle-node unfolding
51
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spelling Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centresMarín, D.Saavedra, M.Villadelprat, J.asymptotic expansionsDulac timePeriod functionsaddle-node unfolding51In 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.2017SGR1617, 2017SGR1725; Ministerio de Ciencia, Innovación y Universidades, MCIU: MTM2017-86795-C3-2-P, PGC2018-095998-B-I00Cambridge University Press2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion9 p.application/pdfhttp://hdl.handle.net/2072/531298RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésProceedings of the Royal Society of Edinburgh Section A: MathematicsL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/5312982026-05-29T05:05:01Z
dc.title.none.fl_str_mv Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres
title Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres
spellingShingle Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres
Marín, D.
asymptotic expansions
Dulac time
Period function
saddle-node unfolding
51
title_short Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres
title_full Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres
title_fullStr Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres
title_full_unstemmed Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres
title_sort Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres
dc.creator.none.fl_str_mv Marín, D.
Saavedra, M.
Villadelprat, J.
author Marín, D.
author_facet Marín, D.
Saavedra, M.
Villadelprat, J.
author_role author
author2 Saavedra, M.
Villadelprat, J.
author2_role author
author
dc.subject.none.fl_str_mv asymptotic expansions
Dulac time
Period function
saddle-node unfolding
51
topic asymptotic expansions
Dulac time
Period function
saddle-node unfolding
51
description 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.
publishDate 2021
dc.date.none.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/531298
url http://hdl.handle.net/2072/531298
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Proceedings of the Royal Society of Edinburgh Section A: Mathematics
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 9 p.
application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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