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Título:
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The three-dimensional center problem for the zero-Hopf singularity
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Autor/a:
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García, I. A. (Isaac A.); Valls, Claudia
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Notas:
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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.
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). |
Materia(s):
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-Zero-Hopf singularity -Three-dimensional vector fields -Continua of periodic orbits -Poincaré map -Matemàtica -Mathematics |
Derechos:
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(c) American Institute of Mathematical Sciences , 2016
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Tipo de documento:
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Artículo Artículo - Versión aceptada |
Editor:
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American Institute of Mathematical Sciences
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