The 1:-2 resonant center problem in the quadratic case is to find necessary and sufficient conditions (on the coefficients) for the existence of a local analytic first integral for the vector field . There are twenty cases of center. Their necessity was proved in [4] using factorization of polynomials with integer coefficients modulo prime numbers. Here we show that, in each of the twenty cases found in [4], there is an analytic first integral. We develop a new method of investigation of analytic properties of polynomial vector fields.
@article{bwmeta1.element.bwnjournal-article-fmv157i2p191bwm,
author = {Alexandra Fronville and Anton Sadovski and Henryk \.Zo\l \k adek},
title = {Solution of the 1 : -2 resonant center problem in the quadratic case},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {191-207},
zbl = {0943.34018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p191bwm}
}
Fronville, Alexandra; Sadovski, Anton; Żołądek, Henryk. Solution of the 1 : −2 resonant center problem in the quadratic case. Fundamenta Mathematicae, Tome 158 (1998) pp. 191-207. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p191bwm/
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