We study the resurgent structure associated with a Hamilton-Jacobi equation. This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via complex matching. We derive the Bridge equation, which encompasses infinitely many resurgent relations satisfied by the formal solution and the other components of the formal integral.
Nous étudions la structure résurgente associée à une équation de Hamilton-Jacobi, qui apparaît en tant qu'équation intérieure dans la méthode de "complex matching" appliquée au problème de l'écart des séparatrices d'un pendule perturbé. Nous obtenons notamment l'équation du pont, qui regroupe une infinité de relations de résurgence satisfaites par la solution formelle et les autres composantes de l'intégrale formelle.
Classification: 34M25, 34M30, 34M37, 37G20, 70H20
Keywords: Hamilton-Jacobi equation, splitting of separatrices, Borel summation, resurgence
@article{AIF_2003__53_4_1185_0, author = {Oliv\'e, Carme and Sauzin, David and Seara, Tere M.}, title = {Resurgence in a {Hamilton-Jacobi} equation}, journal = {Annales de l'Institut Fourier}, pages = {1185--1235}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {4}, year = {2003}, doi = {10.5802/aif.1977}, mrnumber = {2033513}, zbl = {1077.34086}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1977/} }
TY - JOUR TI - Resurgence in a Hamilton-Jacobi equation JO - Annales de l'Institut Fourier PY - 2003 DA - 2003/// SP - 1185 EP - 1235 VL - 53 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1977/ UR - https://www.ams.org/mathscinet-getitem?mr=2033513 UR - https://zbmath.org/?q=an%3A1077.34086 UR - https://doi.org/10.5802/aif.1977 DO - 10.5802/aif.1977 LA - en ID - AIF_2003__53_4_1185_0 ER -
Olivé, Carme; Sauzin, David; Seara, Tere M. Resurgence in a Hamilton-Jacobi equation. Annales de l'Institut Fourier, Volume 53 (2003) no. 4, pp. 1185-1235. doi : 10.5802/aif.1977. https://aif.centre-mersenne.org/articles/10.5802/aif.1977/
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