Global centers of a class of cubic polynomial differential systems
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Abstract
A difficult classical problem in the qualitative theory of differential systems in the plane R2 is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center p such that R2\{p} is filled with periodic orbits. In this paper we classify the global centers of the family of real polynomial differential systems of degree 3 that in complex notation write (Formula presented.) where w=x+iy and Ak∈C for k=3,4,5,6.
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34C05, Global centers, Polynomial differential equations, Vertical blow-up
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English
Citation
Rendiconti del Circolo Matematico di Palermo, v. 73, n. 5, p. 2141-2160, 2024.
