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dc.contributor.authorAlgaba Durán, Antonio 
dc.contributor.authorGamero, Estanislao
dc.contributor.authorGarcía García, Cristóbal
dc.identifier.citationAlgaba, A., Gamero, E., & García, C. (2021). Orbital Hypernormal Forms. Symmetry, 13(8), 1500.
dc.identifier.issn2073-8994 (electrónico)
dc.description.abstractIn this paper, we analyze the problem of determining orbital hypernormal forms—that is, the simplest analytical expression that can be obtained for a given autonomous system around an isolated equilibrium point through time-reparametrizations and transformations in the state variables. We show that the computation of orbital hypernormal forms can be carried out degree by degree using quasi-homogeneous expansions of the vector field of the system by means of reduced time-reparametrizations and near-identity transformations, achieving an important reduction in the computational effort. Moreover, although the orbital hypernormal form procedure is essentially nonlinear in nature, our results show that orbital hypernormal forms are characterized by means of linear operators. Some applications are considered: the case of planar vector fields, with emphasis on a case of the Takens–Bogdanov singularityes_ES
dc.relation.isversionofPublisher’s version
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.subject.otherOrbital normal formses_ES
dc.subject.otherHomological operatorses_ES
dc.subject.otherLie symmetrieses_ES
dc.subject.otherNilpotent centerses_ES
dc.titleOrbital Hypernormal Formses_ES
dc.subject.unesco12 Matemáticases_ES

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