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arXiv · 1705.07731

A counterexample to the composition condition conjecture for polynomial Abel differential equations

Jaume Giné·Maite Grau·Xavier Santallusia
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Abstract

The Polynomial Abel differential equations are considered a model problem for the classical Poincaré center--focus problem for planar polynomial systems of ordinary differential equations. Last decades several works pointed out that all the centers of the polynomial Abel differential equations satisfied the composition conditions (also called universal centers). In this work we provide a simple counterexample to this conjecture.

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Jaume Giné, Maite Grau, Xavier Santallusia. 2017-05-15. A counterexample to the composition condition conjecture for polynomial Abel differential equations. https://arxiv.org/abs/1705.07731

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