Commutators and linearizations of isochronous centers
Mazzi, Luisa ; Sabatini, Marco
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 11 (2000), p. 81-98 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

Si studiano centri isocroni di alcune classi di sistemi differenziali piani. Si considerano sistemi con velocità angolare costante, sia con nonlinearità omogenee, sia con nonlinearità non omogenee. Si mostra come, a partire da un commutatore, sia possibile costruire una linearizzazione ed un integrale primo. Si trovano commutatori per alcune classi di sistemi. I risultati ottenuti vengono applicati per dimostrare l’isocronia di alcune classi di centri, e per trovare integrali primi per una classe di equazioni di Liénard con centri isocroni.

Publié le : 2000-06-01
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     author = {Luisa Mazzi and Marco Sabatini},
     title = {Commutators and linearizations of isochronous centers},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {11},
     year = {2000},
     pages = {81-98},
     zbl = {0973.34020},
     mrnumber = {1797513},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2000_9_11_2_81_0}
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Mazzi, Luisa; 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, Tome 11 (2000) pp. 81-98. http://gdmltest.u-ga.fr/item/RLIN_2000_9_11_2_81_0/

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