dc.contributor.author |
García, I. A. (Isaac A.) |
dc.contributor.author |
Valls, Claudia |
dc.date |
2016-11-08T14:28:10Z |
dc.date |
2016-03-01 |
dc.date |
2016-11-08T14:28:10Z |
dc.identifier |
1078-0947 |
dc.identifier |
http://hdl.handle.net/10459.1/58428 |
dc.identifier |
https://doi.org/10.3934/dcds.2016.36.2027 |
dc.identifier.uri |
http://hdl.handle.net/10459.1/58428 |
dc.description |
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 |
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 |
application/pdf |
dc.language |
eng |
dc.publisher |
American Institute of Mathematical Sciences |
dc.relation |
MINECO/PN2013-2016/MTM2014-53703-P |
dc.relation |
Versió postprint del document publicat a https://doi.org/10.3934/dcds.2016.36.2027 |
dc.relation |
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 |
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 |
Matemàtica |
dc.subject |
Mathematics |
dc.title |
The three-dimensional center problem for the zero-Hopf singularity |
dc.type |
info:eu-repo/semantics/article |
dc.type |
info:eu-repo/semantics/acceptedVersion |