RT Journal Article
T1 Orbital Hypernormal Forms
A1 Algaba Durán, Antonio
A1 Gamero, Estanislao
A1 García García, Cristóbal
AB In 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 singularity
PB MDPI
SN 2073-8994 (electrónico)
YR 2021
FD 2021
LK http://hdl.handle.net/10272/20056
UL http://hdl.handle.net/10272/20056
LA eng
NO Algaba, A., Gamero, E., & García, C. (2021). Orbital Hypernormal Forms. Symmetry, 13(8), 1500. https://doi.org/10.3390/sym13081500
DS Repositorio Institucional de la Universidad de Huelva
RD 31 may 2026