Geodesic
About some equations of the third order with six poles
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2003), pp. 59-68 
A. V. Chichurin. About some equations of the third order with six poles. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2003), pp. 59-68. http://geodesic.mathdoc.fr/item/BASM_2003_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Investigating ordinary differential equations of the third order on the subject of belonging to P-type (solutions of such equations have no movable critical singular points), Chazy has built an equation (Chazy equation) with 32 coefficients. If these coefficients satisfy the special (S)-system, then Chazy equation belongs to P-type. In this paper we find three solution of the (S)-system and build three classes of Chazy equation of the P-type.

[1] Chazy J., “Sur les equations differentielles du troisieme ordre et d'ordre superieur, don't l'integrale generale a ses points critiques fixes”, Acta Math., 34 (1911), 317–385 | DOI | MR | Zbl

[2] Dobrovolskii V. A., Essays of development of analytical theory of differential equations, Kiev, 1974

[3] Lukashevich N. A., “To a theory of the Chazy equation”, Differential Equations, 29:2 (1993), 353–357 | MR

[4] Chichurin A. V., “About one solution of the Chazy system”, Vestnic Brest Univ., 2000, no. 6, 27–34

[5] Chichurin A. V., “Third Order $P$-type equations with six poles”, Vestnic Brest Univ., 2001, no. 2, 55–61 | MR