Generalized nonlinear superposition principles for polynomial planar vector fields.
García, Isaac A., Giacomini, Hector, Giné, Jaume (2005)
Journal of Lie Theory
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Displaying similar documents to “Center conditions for a simple class of quintic systems.”
Generalized nonlinear superposition principles for polynomial planar vector fields.
Application of Chapligin's theorem to autonomous systems.
Radasin, Zvezdana (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C.
Colin Christopher, Christiane Rousseau (2001)
Publicacions Matemàtiques
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In this paper we consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions for linearizability for the class of complex quadratic systems and for the class of complex cubic systems symmetric with respect to a centre. The sufficiency of these conditions is shown by exhibiting explicitly a linearizing change of coordinates, either of Darboux type or a generalization of it. ...
On the complex and real Hessian polynomials.
Martínez-Ojeda, Emigdio, Ortiz-Rodríguez, Adriana (2010)
International Journal of Mathematics and Mathematical Sciences
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On centers of type of polynomial systems
Roberto Conti (1990)
Archivum Mathematicum
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Implicit Differential Equations From the Singularity Theory Viewpoint
J. Bruce, F. Tari (1996)
Banach Center Publications
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Exact solutions for certain nonlinear autonomous ordinary differential equations of the second order and families of two-dimensional autonomous systems.
Markakis, M.P. (2010)
International Journal of Differential Equations
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Solving Equations, an Elegant Legacy
Jerry L. Kazdan (2001)
The Teaching of Mathematics
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Commutators and linearizations of isochronous centers
Luisa Mazzi, Marco Sabatini (2000)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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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...