A characterization of isochronous centres in terms of symmetries.

Freire, Emilio, and Gasull, Armengol, Guillamon, Antoni 2. "A characterization of isochronous centres in terms of symmetries.." Revista Matemática Iberoamericana 20.1 (2004): 205-222. <http://eudml.org/doc/39635>.

@article{Freire2004,
abstract = {We present a description of isochronous centres of planar vector fields X by means of their groups of symmetries. More precisely, given a normalizer U of X (i.e., [X,U]= µ X, where µ is a scalar function), we provide a necessary and sufficient isochronicity condition based on µ. This criterion extends the result of Sabatini and Villarini that establishes the equivalence between isochronicity and the existence of commutators ([X,U]= 0). We put also special emphasis on the mechanical aspects of isochronicity; this point of view forces a deeper insight into the potential and quadratic-like Hamiltonian systems. For these families we provide new ways to find isochronous centres, alternative to those already known from the literature.},
author = {Freire, Emilio, Gasull, Armengol, Guillamon, Antoni 2},
journal = {Revista Matemática Iberoamericana},
keywords = {Campos vectoriales; Sistema hamiltoniano; Período orbital; Grupos de simetría; Sistemas dinámicos; quadratic-like Hamiltonian systems; isochronous centres},
language = {eng},
number = {1},
pages = {205-222},
title = {A characterization of isochronous centres in terms of symmetries.},
url = {http://eudml.org/doc/39635},
volume = {20},
year = {2004},
}

TY - JOUR
AU - Freire, Emilio
AU - Gasull, Armengol, Guillamon, Antoni 2
TI - A characterization of isochronous centres in terms of symmetries.
JO - Revista Matemática Iberoamericana
PY - 2004
VL - 20
IS - 1
SP - 205
EP - 222
AB - We present a description of isochronous centres of planar vector fields X by means of their groups of symmetries. More precisely, given a normalizer U of X (i.e., [X,U]= µ X, where µ is a scalar function), we provide a necessary and sufficient isochronicity condition based on µ. This criterion extends the result of Sabatini and Villarini that establishes the equivalence between isochronicity and the existence of commutators ([X,U]= 0). We put also special emphasis on the mechanical aspects of isochronicity; this point of view forces a deeper insight into the potential and quadratic-like Hamiltonian systems. For these families we provide new ways to find isochronous centres, alternative to those already known from the literature.
LA - eng
KW - Campos vectoriales; Sistema hamiltoniano; Período orbital; Grupos de simetría; Sistemas dinámicos; quadratic-like Hamiltonian systems; isochronous centres
UR - http://eudml.org/doc/39635
ER -