We study integrability of two-dimensional autonomous systems in the plane with center type linear part. For quadratic and homogeneous cubic systems we give a simple characterization for integrable cases, and we find explicitly all first integrals for these cases. Finally, two large integrable system classes are determined in the most general nonhomogeneous cases.
@article{bwmeta1.element.bwnjournal-article-zmv22z2p285bwm,
author = {Javier Chavarriga},
title = {Integrable systems in the plane with center type linear part},
journal = {Applicationes Mathematicae},
volume = {22},
year = {1994},
pages = {285-309},
zbl = {0809.34002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv22z2p285bwm}
}
Chavarriga, Javier. Integrable systems in the plane with center type linear part. Applicationes Mathematicae, Tome 22 (1994) pp. 285-309. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv22z2p285bwm/
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