Geodesic
On solutions of the chazy equation
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2021), pp. 51-59

Voir la notice de l'article provenant de la source Math-Net.Ru

The Chazy system determines the necessary and sufficient conditions for the absence of movable critical points of solutions of the particular third order differential equation that was considered by Chazy in one of the first papers on the classification of higher-order ordinary differential equations with respect to the Painlevé property. The solution of the complete Chazy system in the case of constant poles has been already obtained. However, the question of integrating the Chazy equation remained open until now. In this paper, we prove that in the case of constant poles, under some additional conditions, this equation is integrated in elliptic functions.
Keywords: Chazy equation; Chazy system; Painlevé property; elliptic functions. 
@article{BGUMI_2021_2_a4,
     author = {K. G. Atrokhau and E. V. Gromak},
     title = {On solutions of the chazy equation},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {51--59},
     publisher = {mathdoc},
     volume = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2021_2_a4/}
}
TY  - JOUR
AU  - K. G. Atrokhau
AU  - E. V. Gromak
TI  - On solutions of the chazy equation
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2021
SP  - 51
EP  - 59
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2021_2_a4/
LA  - en
ID  - BGUMI_2021_2_a4
ER  - 
%0 Journal Article
%A K. G. Atrokhau
%A E. V. Gromak
%T On solutions of the chazy equation
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2021
%P 51-59
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BGUMI_2021_2_a4/
%G en
%F BGUMI_2021_2_a4
K. G. Atrokhau; E. V. Gromak. On solutions of the chazy equation. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2021), pp. 51-59. http://geodesic.mathdoc.fr/item/BGUMI_2021_2_a4/