Center problem in the center manifold for quadratic differential systems in R^3

Abstract

Using tools of computer algebra based on the Gröbner basis theory we derive conditions for the existence of a center on a local center manifold for fifteen seven-parameter families of quadratic systems on R 3. To obtain the results we use modular arithmetics.

The authors are grateful to the referees for their valuable remarks which helped to improve the manuscript. The first author is partially supported by a MINECO/ FEDER grant number MTM2014-53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. The second author is supported by Portuguese National Funds through FCT - Fundación para a Ciéncia e a Tecnología within the project PEst-OE/EEI/LA0009/2013 (CAMGSD).