Global phase portraits of uniform isochronous centers with quartichomogeneous polynomial nonlinearities
Copyright policy )Global phase portraits of uniform isochronous centers with quartichomogeneous polynomial nonlinearities
Agraïments: The first author is is supported by a Ciência sem Fronteiras-CNPq grant number 201002/ 2012-4. A CAPES grant number 88881.030454/2013-01 from the program CSF-PVE We classify the global phase portraits in the Poincar\'e disc of the differential systems =-y xf(x,y), =x yf(x,y), where f(x,y) is a homogeneous polynomial of degree 3. These systems have a uniform isochronous center at the origin. This paper together with the results presented in IL2 completes the classification of the global phase portraits in the Poincar\'e disc of all quartic polynomial differential systems with a uniform isochronous center at the origin.
uniform isochronous center, Polynomial vector field, polynomial vector field, Poincaré disk, quartic polynomial differential system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, phase portrait, Uniform isochronous center, Periodic solutions to ordinary differential equations, Phase portrait
uniform isochronous center, Polynomial vector field, polynomial vector field, Poincaré disk, quartic polynomial differential system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, phase portrait, Uniform isochronous center, Periodic solutions to ordinary differential equations, Phase portrait
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