<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This is a brief survey on the centers of the analytic differential systems in ℝ<sup>2</sup>. First we consider the kind of integrability of the different types of centers, and after we analyze the focus–center problem, i.e. how to distinguish a center from a focus. This is a difficult problem which is not completely solved. We shall present some recent results using the divergence of the differential system.</p></abstract>

This is a brief survey on the centers of the analytic differential systems in ℝ2. First we consider the kind of integrability of the different types of centers, and after we analyze the focus–center problem, i.e. how to distinguish a center from a focus. This is a difficult problem which is not completely solved. We shall present some recent results using the divergence of the differential system.

Centers: their integrability and relations with the divergence

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Centers: their integrability and relations with the divergence"}

This is a brief survey on the centers of the analytic differential systems in ℝ2. First we consider the kind of integrability of the different types of...

Centers: their integrability and relations with the divergence

Published Online: Jan 01, 2016

Page range: 79 - 86

Received: Oct 03, 2015

Accepted: Nov 19, 2015

DOI: https://doi.org/10.21042/AMNS.2016.1.00007

© 2016 J. Llibre, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.