The three-dimensional center problem for the zero-Hopf singularity
| dc.contributor.author | García, I. A. (Isaac A.) | |
| dc.contributor.author | Valls, Claudia | |
| dc.date.accessioned | 2016-11-08T14:28:10Z | |
| dc.date.issued | 2016-03-01 | |
| dc.date.updated | 2016-11-08T14:28:10Z | |
| dc.description.abstract | In this work we extend well-known techniques for solving the Poincar\'e-Lyapunov nondegenerate analytic center problem in the plane to the 3-dimensional center problem at the zero-Hopf singularity. Thus we characterize the existence of a neighborhood of the singularity completely foliated by periodic orbits (including continua of equilibria) via an analytic Poincar\'e return map. The vanishing of the first terms in a Taylor expansion of the associated displacement map provides us with the necessary 3-dimensional center conditions in the parameter space of the family whereas the sufficiency is obtained through symmetry-integrability methods. Finally we use the proposed method to classify the 3-dimensional centers of some quadratic polynomial differential families possessing a zero-Hopf singularity. | |
| dc.description.sponsorship | The first author is partially supported by a MINECO grant number MTM2014-53703-P and by a CIRIT grant number 2014 SGR 1204. The second author is partially supported by Portuguese national funds through FCT - Fundaçao para a Ciéncia e a Tecnologia: project UID/MAT/04459/2013 (CAMGSD). | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.doi | https://doi.org/10.3934/dcds.2016.36.2027 | |
| dc.identifier.idgrec | 023236 | |
| dc.identifier.issn | 1078-0947 | |
| dc.identifier.uri | http://hdl.handle.net/10459.1/58428 | |
| dc.language.iso | eng | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.relation | MINECO/PN2013-2016/MTM2014-53703-P | |
| dc.relation.isformatof | Versió postprint del document publicat a https://doi.org/10.3934/dcds.2016.36.2027 | |
| dc.relation.ispartof | Discrete and Continuous Dynamical Systems Series A, 2016, vol. 36, núm. 4, p. 2027-2046 | |
| dc.rights | (c) American Institute of Mathematical Sciences , 2016 | |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Zero-Hopf singularity | |
| dc.subject | Three-dimensional vector fields | |
| dc.subject | Continua of periodic orbits | |
| dc.subject | Poincaré map | |
| dc.subject.classification | Matemàtica | |
| dc.subject.other | Mathematics | |
| dc.title | The three-dimensional center problem for the zero-Hopf singularity | |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion |