Tissus du plan et polynômes de Darboux

Olivier Ripoll[1]; Julien Sebag[2]

  • [1] Université Bordeaux 1, 351 cours de la Libération, 33405 Talence
  • [2] Université Rennes 1, UFR Mathématiques, IRMAR, 263 avenue du General Leclerc, CS 74205, 35042 Rennes cedex (France)

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

  • Volume: 19, Issue: 1, page 1-11
  • ISSN: 0240-2963

Abstract

top
In this article, we study the problem of the existence of Darboux polynomials in C { x } y , y ′ for the derivation δ = R ( y ) ∂ x + R ( y ) y ′ ∂ y - V ( y , y ′ ) ∂ y ′ .

How to cite

top

Ripoll, Olivier, and Sebag, Julien. "Tissus du plan et polynômes de Darboux." Annales de la faculté des sciences de Toulouse Mathématiques 19.1 (2010): 1-11. <http://eudml.org/doc/115863>.

@article{Ripoll2010,
abstract = {Dans cet article, nous étudions le problème de l’existence de polynômes de Darboux dans $\mathbf\{C\}\lbrace x\rbrace \left[y,y^\{\prime\}\right]$ pour la dérivation $\delta =R(y)\partial _x+R(y)y^\{\prime\}\partial _y-V(y,y^\{\prime\})\partial _\{y^\{\prime\}\}$.},
affiliation = {Université Bordeaux 1, 351 cours de la Libération, 33405 Talence; Université Rennes 1, UFR Mathématiques, IRMAR, 263 avenue du General Leclerc, CS 74205, 35042 Rennes cedex (France)},
author = {Ripoll, Olivier, Sebag, Julien},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {-web; Darboux polynomial},
language = {fre},
month = {1},
number = {1},
pages = {1-11},
publisher = {Université Paul Sabatier, Toulouse},
title = {Tissus du plan et polynômes de Darboux},
url = {http://eudml.org/doc/115863},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Ripoll, Olivier
AU - Sebag, Julien
TI - Tissus du plan et polynômes de Darboux
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2010/1//
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - 1
SP - 1
EP - 11
AB - Dans cet article, nous étudions le problème de l’existence de polynômes de Darboux dans $\mathbf{C}\lbrace x\rbrace \left[y,y^{\prime}\right]$ pour la dérivation $\delta =R(y)\partial _x+R(y)y^{\prime}\partial _y-V(y,y^{\prime})\partial _{y^{\prime}}$.
LA - fre
KW - -web; Darboux polynomial
UR - http://eudml.org/doc/115863
ER -

References

top
  1. Carnicer (M. M.).— The Poincaré problem in the nondicritical case. Ann. of Math. (2) 140, no. 2, p. 289-294 (1994). Zbl0821.32026MR1298714
  2. Casale (G.).— Irréductibilité de la première équation de Painlevé. (French) [Irreducibility of the first Painleve equation] C. R. Math. Acad. Sci. Paris 343, no. 2, p. 95-98 (2006). Zbl1101.34339MR2242039
  3. Cerveau (D.), Lins Neto (A.).— Holomorphic foliations in C P ( 2 ) having an invariant algebraic curve. Ann. Inst. Fourier (Grenoble) 41, no. 4, p. 883-903 (1991). Zbl0734.34007MR1150571
  4. Hénaut (A.).— On planar web geometry through abelian relations and connections, Ann. of Math. 159, p. 425-445 (2004). Zbl1069.53020MR2052360
  5. Hénaut (A.).— Caractérisation des tissus de  C 2 dont le rang est maximal et qui sont linéarisables, Compositio Math. 94 , p. 247-268 (1994). Zbl0877.53013MR1310859
  6. Moulin Ollagnier (J.), Nowicki (A.) and Strelcyn (J.-M.).— On the non-existence of constants of derivations : the proof of a theorem of Jouanolou and its development. Bull. Sci. math. 119, p. 195-233 (1995). Zbl0855.34010MR1327804
  7. Nishioka (K.).— A note on the transcendency of Painlevé’s first transcendent. Nagoya Math. J. 109, p. 63-67 (1988). Zbl0613.34030MR931951
  8. Prelle (M.J.) and Singer (M.F.).— Elementary First Integrals of Differential Equations, Trans. Amer. Math. Soc., 279 (1), p. 215-229 (1983). Zbl0527.12016MR704611
  9. Ripoll (O.).— Détermination du rang des tissus du plan et autres invariants géométriques, C.R. Acad. Sci. Paris, Ser. I 341, p. 247-252 (2005). Zbl1088.53006MR2164681
  10. Ripoll (O.).— Properties of the connection associated with planar webs and applications, à paraître, Arxiv math.DG/0702321. 
  11. Ripoll (O.) et Sebag (J.).— Solutions singulières des tissus polynomiaux du plan, J. of Algebra 310, p. 351-370 (2007). Zbl1141.53013MR2307797
  12. Umemura (H.).— Second proof of the irreducibility of the first differential equation of Painlevé. Nagoya Math. J. 117, p. 125-171 (1990). Zbl0688.34006MR1044939
  13. Grifone (J.) and Salem (É.) (Eds).— Web Theory and Related Topics, World Scientific, Sci. Publishing co., River Edge, NJ, (2001). Zbl0983.00024MR1837880

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.