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- Tome 31 (2024)

- no. 1

- p. 65-82

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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.

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.

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Jacky Cresson 1 ; Jordy Palafox 2

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