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...
| Authors: | ; ; |
|---|---|
| Format: | Article |
| Status: | Accepted version |
| Publication date: | 2021 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/531298 |
| Online Access: | http://hdl.handle.net/2072/531298 |
| Access Level: | Open access |
| Keyword: | asymptotic expansions Dulac time Period function saddle-node unfolding 51 |
| _version_ | 1878741233459789824 |
|---|---|
| author | Marín, D. |
| author2 | Saavedra, M. Villadelprat, J. |
| author2_role | author author |
| author_browse | Marín, D. Saavedra, M. Villadelprat, J. |
| author_facet | Marín, D. Saavedra, M. Villadelprat, J. |
| author_role | author |
| collection | Recercat. Dipósit de la Recerca de Catalunya |
| 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_e18c8dedbed758d5e5da9698ece9bdfd |
| institution | 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) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:recercat.cat:2072/531298 |
| publishDate | 2021 |
| publishDateSort | 2021 |
| publisher | Cambridge University Press |
| publisherStr | Cambridge University Press |
| reponame_str | Recercat. Dipósit de la Recerca de Catalunya |
| spelling | Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres Marín, D. Saavedra, M. Villadelprat, J. asymptotic expansions Dulac time Period function saddle-node unfolding 51 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. 2017SGR1617, 2017SGR1725; Ministerio de Ciencia, Innovación y Universidades, MCIU: MTM2017-86795-C3-2-P, PGC2018-095998-B-I00 Cambridge University Press http://hdl.handle.net/2072/531298 |
| 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 |
| status_str | acceptedVersion |
| title | 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_short | 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 |
| topic | asymptotic expansions Dulac time Period function saddle-node unfolding 51 |
| topic_facet | asymptotic expansions Dulac time Period function saddle-node unfolding 51 |
| url | http://hdl.handle.net/2072/531298 |