Commutators and linearizations of isochronous centers

Luisa Mazzi; Marco Sabatini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2000)

  • Volume: 11, Issue: 2, page 81-98
  • ISSN: 1120-6330

Abstract

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We study isochronous centers of some classes of plane differential systems. We consider systems with constant angular speed, both with homogeneous and nonhomogenous nonlinearities. We show how to construct linearizations and first integrals of such systems, if a commutator is known. Commutators are found for some classes of systems. The results obtained are used to prove the isochronicity of some classes of centers, and to find first integrals for a class of Liénard equations with isochronous centers.

How to cite

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Mazzi, Luisa, and Sabatini, Marco. "Commutators and linearizations of isochronous centers." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 11.2 (2000): 81-98. <http://eudml.org/doc/252342>.

@article{Mazzi2000,
abstract = {We study isochronous centers of some classes of plane differential systems. We consider systems with constant angular speed, both with homogeneous and nonhomogenous nonlinearities. We show how to construct linearizations and first integrals of such systems, if a commutator is known. Commutators are found for some classes of systems. The results obtained are used to prove the isochronicity of some classes of centers, and to find first integrals for a class of Liénard equations with isochronous centers.},
author = {Mazzi, Luisa, Sabatini, Marco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Polynomial systems; Isochronous centers; Commuting vector fields; Linearizations; First integrals; Liénard systems; isochronous center; Liénard system},
language = {eng},
month = {6},
number = {2},
pages = {81-98},
publisher = {Accademia Nazionale dei Lincei},
title = {Commutators and linearizations of isochronous centers},
url = {http://eudml.org/doc/252342},
volume = {11},
year = {2000},
}

TY - JOUR
AU - Mazzi, Luisa
AU - Sabatini, Marco
TI - Commutators and linearizations of isochronous centers
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2000/6//
PB - Accademia Nazionale dei Lincei
VL - 11
IS - 2
SP - 81
EP - 98
AB - We study isochronous centers of some classes of plane differential systems. We consider systems with constant angular speed, both with homogeneous and nonhomogenous nonlinearities. We show how to construct linearizations and first integrals of such systems, if a commutator is known. Commutators are found for some classes of systems. The results obtained are used to prove the isochronicity of some classes of centers, and to find first integrals for a class of Liénard equations with isochronous centers.
LA - eng
KW - Polynomial systems; Isochronous centers; Commuting vector fields; Linearizations; First integrals; Liénard systems; isochronous center; Liénard system
UR - http://eudml.org/doc/252342
ER -

References

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