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

Published online by Cambridge University Press:  13 March 2018

JAUME GINÉ Open the ORCID record for JAUME GINÉ [Opens in a new window] ,
MAITE GRAU  and
XAVIER SANTALLUSIA
JAUME GINÉ
Affiliation:
Departament de Matemàtica, Inspires Research Centre, Universitat de Lleida, Avda Jaume II, 69; 25001 Lleida, Catalonia, Spain email gine@matematica.udl.cat, mtgrau@matematica.udl.cat, xivaer@gmail.com
MAITE GRAU
Affiliation:
Departament de Matemàtica, Inspires Research Centre, Universitat de Lleida, Avda Jaume II, 69; 25001 Lleida, Catalonia, Spain email gine@matematica.udl.cat, mtgrau@matematica.udl.cat, xivaer@gmail.com
XAVIER SANTALLUSIA
Affiliation:
Departament de Matemàtica, Inspires Research Centre, Universitat de Lleida, Avda Jaume II, 69; 25001 Lleida, Catalonia, Spain email gine@matematica.udl.cat, mtgrau@matematica.udl.cat, xivaer@gmail.com
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Abstract

Polynomial Abel differential equations are considered a model problem for the classical Poincaré center–focus problem for planar polynomial systems of ordinary differential equations. In the last few decades, several works pointed out that all 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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 12 , December 2019 , pp. 3347 - 3352
Copyright
© Cambridge University Press, 2018 

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