On algebraic solutions of algebraic Pfaff equations
Żołądek, Henryk
Studia Mathematica, Tome 113 (1995), p. 117-126 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system ẋ=zs,ẏ=xs,ż=ys. We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:216183 
@article{bwmeta1.element.bwnjournal-article-smv114i2p117bwm,
     author = {Henryk \.Zo\l \k adek},
     title = {On algebraic solutions of algebraic Pfaff equations},
     journal = {Studia Mathematica},
     volume = {113},
     year = {1995},
     pages = {117-126},
     zbl = {0826.34003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv114i2p117bwm}
}

Żołądek, Henryk. On algebraic solutions of algebraic Pfaff equations. Studia Mathematica, Tome 113 (1995) pp. 117-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv114i2p117bwm/

[00000] [1] A. A. Andronov, E. A. Leontovich, I. I. Gordon and A. G. Maier, Qualitative Theory of Dynamical Systems of Second Order, Moscow, Nauka, 1966 (in Russian).

[00001] [2] M. Carnicer, The Poincaré problem in the dicritical case, Ann. of Math. 140 (1994), 289-294. | Zbl 0821.32026

[00002] [3] D. Cerveau and A. Lins-Neto, Holomorphic foliations in CP(2) having an invariant algebraic curve, Ann. Inst. Fourier (Grenoble) 41 (4) (1991), 883-903. | Zbl 0734.34007

[00003] [4] G. Darboux, Mémoire sur les équations différentielles algébriques du premier ordre et du premier degré, Bull. Sci. Math. (Mélanges) 1878, 60-96; 123-144; 151-200. | Zbl 10.0214.01

[00004] [5] J. P. Jouanolou, Equations de Pfaff algébriques, Lecture Notes in Math. 708, Springer, 1979.

[00005] [6] A. Lins-Neto, Algebraic solutions of polynomial differential equations and foliations in dimension two, in: Holomorphic Dynamics, Lecture Notes in Math. 1345, Springer, 1988, 193-232 | Zbl 0677.58036

[00006] [7] J. Moulin-Ollagnier, A. Nowicki and J.-M. Strelcyn, On non-existence of constants of derivations; the proof of Jouanolou theorem and its development, preprint, 1992. | Zbl 0855.34010

[00007] [8] H. Żołądek, The solution of the center-focus problem, preprint, 1992.