Artículo
Orbital Hypernormal Forms
Autor/es | Algaba Durán, Antonio
Gamero Gutiérrez, Estanislao ![]() ![]() ![]() ![]() ![]() ![]() García García, Cristóbal |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Fecha de publicación | 2021-08 |
Fecha de depósito | 2022-10-17 |
Publicado en |
|
Resumen | 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 ... 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. |
Agencias financiadoras | Ministerio de Ciencia, Innovación y Universidades (MICINN). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Junta de Andalucía |
Identificador del proyecto | MTM2017-87915-C2-1-P
![]() PGC2018-096265-B-I00 ![]() P12-FQM-1658 ![]() UHU-1260150 ![]() TIC-130 ![]() FQM-276 ![]() |
Cita | Algaba Durán, A., Gamero Gutiérrez, E. y García García, C. (2021). Orbital Hypernormal Forms. Symmetry, 13 (8), 1500. https://doi.org/10.3390/sym13081500. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
Orbital hypernormal forms.pdf | 399.0Kb | ![]() | Ver/ | |