Displaying similar documents to “Uniformly isochronous polynomial centers.”

Chaos in some planar nonautonomous polynomial differential equation

Klaudiusz Wójcik (2000)

Annales Polonici Mathematici

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We show that under some assumptions on the function f the system ż = z ̅ ( f ( z ) e i ϕ t + e i 2 ϕ t ) generates chaotic dynamics for sufficiently small parameter ϕ. We use the topological method based on the Lefschetz fixed point theorem and the Ważewski retract theorem.

Integrability of a linear center perturbed by a fifth degree homogeneous polynomial.

Javier Chavarriga, Jaume Giné (1997)

Publicacions Matemàtiques

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In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

Integrability of a linear center perturbed by a fourth degree homogeneous polynomial.

Javier Chavarriga, Jaume Giné (1996)

Publicacions Matemàtiques

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In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.