We obtain new proof of several results of Alain Hénaut (Lie Symmetries for Implicit Planar Webs, J. Math. Sci. Univ Tokyo 29(1):155–148, 2022) using the framework of actions of Lie groups on differential equations. We compute explicitly several symmetry groups for known webs. We also precise the link existing between the Lie algebra of symmetries of a given web and the existence of Darboux polynomials.
On retrouve plusieurs résultats de Alain Hénaut (Lie Symmetries for Implicit Planar Webs, J. Math. Sci. Univ Tokyo 29(1) :155–148, 2022) sur les groupes de symétrie des tissus implicites dans le cadre usuel des actions de groupes de Lie sur les équations différentielles. On calcule explicitement les groupes de symétries de tissus particuliers. On donne aussi un lien entre l’algèbre de Lie des symétries d’un tissu et l’existence de polynômes de Darboux.
Jacky Cresson 1; Jordy Palafox 2
@article{AMBP_2024__31_1_65_0, author = {Jacky Cresson and Jordy Palafox}, title = {Application des groupes de {Lie} \`a la recherche des sym\'etries des tissus implicites du plan}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {65--82}, publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal}, volume = {31}, number = {1}, year = {2024}, doi = {10.5802/ambp.426}, language = {fr}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.426/} }
TY - JOUR AU - Jacky Cresson AU - Jordy Palafox TI - Application des groupes de Lie à la recherche des symétries des tissus implicites du plan JO - Annales mathématiques Blaise Pascal PY - 2024 SP - 65 EP - 82 VL - 31 IS - 1 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.426/ DO - 10.5802/ambp.426 LA - fr ID - AMBP_2024__31_1_65_0 ER -
%0 Journal Article %A Jacky Cresson %A Jordy Palafox %T Application des groupes de Lie à la recherche des symétries des tissus implicites du plan %J Annales mathématiques Blaise Pascal %D 2024 %P 65-82 %V 31 %N 1 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.426/ %R 10.5802/ambp.426 %G fr %F AMBP_2024__31_1_65_0
Jacky Cresson; Jordy Palafox. Application des groupes de Lie à la recherche des symétries des tissus implicites du plan. Annales mathématiques Blaise Pascal, Volume 31 (2024) no. 1, pp. 65-82. doi : 10.5802/ambp.426. https://ambp.centre-mersenne.org/articles/10.5802/ambp.426/
[1] Géométrie des tissus (d’après S.S. Chern et P.A. Griffins, Séminaire Bourbaki, 31e année, 1978/79 (Lecture Notes in Mathematics), Volume 770, Springer, 1979, pp. 103-119 | Zbl
[2] Geometrie der Gewebe. Topologische Fragen der Differentialgeometrie, Grundlehren der Mathematischen Wissenschaften, Springer, 1938
[3] Discriminants, Resultants and Multidimensional Determinants, Mathematics : Theory & Applications, Birkhäuser, 1994 | DOI
[4] Sur le théorème de Maillet, Funkc. Ekvacioj, Ser. Int., Volume 34 (1991) no. 1, pp. 117-125 | Zbl
[5] Singular Nonlinear Partial Differential Equations, Aspects of Mathematics, E28, Vieweg, 1996 | DOI
[6] Formal Power Series Solutions of Nonlinear First Order Partial Differential Equations, Funkc. Ekvacioj, Ser. Int., Volume 41 (1998) no. 1, pp. 133-166 | Zbl
[7] On the Blaschke conjecture for 3-webs, J. Geom. Anal., Volume 16 (2006) no. 1, pp. 69-115 | DOI | Zbl
[8] On the linearizability of 3-webs, Nonlinear Anal., Theory Methods Appl., Volume 47 (2001) no. 4, pp. 2643-2654 | DOI | Zbl
[9] On planar web geometry through abelian relations and connections, Ann. Math., Volume 159 (2004) no. 1, pp. 425-445 | DOI | Zbl
[10] Lie Symmetries for Implicit Planar Webs, J. Math. Sci., Tokyo, Volume 29 (2022) no. 1, pp. 115-148 | Zbl
[11] Lectures on Analytic Differential Equations, Graduate Studies in Mathematics, 86, American Mathematical Society, 2008 | Zbl
[12] On the linearizability of 3-webs : End of controversy, C. R. Math. Acad. Sci. Paris, Volume 356 (2018) no. 1, pp. 97-99 | DOI | Zbl
[13] Equivalence, Invariants and Symmetry, Cambridge University Press, 1995 | DOI
[14] Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, 107, Springer, 1998
[15] An Invitation to Web Geometry, IMPA Monographs, 2, Springer, 2015 | DOI
[16] Theory of logarithmic differential forms and logarithmic vector fields, J. Fac. Sci., Univ. Tokyo, Sect. I A, Volume 27 (1980), pp. 265-291 | Zbl
[17] Un teoreme topologico sulle schiere di curve e une caratterizzazione geometrica sulle superficie isotermo-asintotiche, Boll. Unione Mat. Ital., Volume 6 (1927), pp. 80-85 | Zbl
Cited by Sources: