Resurgence of inner solutions for perturbations of the McMillan map

Discrete and Continuous Dynamical Systems

Volumn 31, Issue 1, 2011, Pages 165-207

  Martín, Pau ^a   Sauzin, David ^b   Seara, Tere M ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b OBSERVATOIRE DE PARIS   (France)

Author keywords

Exponentially small phenomena; Resurgence; Splitting of separatrices

Indexed keywords

EID: 84859521607     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2011.31.165     Document Type: Article

References (7)

1. B. Candelpergher, J.-C. Nosmas and F. Pham, "Approche de la Ŕesurgence," (French) [Ap- proach to resurgence] Actualit́es Math́ematiques, [Current Mathematical Topics] Hermann, Paris, 1993.
2. J. Ecalle, "Les Fonctions Ŕesurgentes. Tome I," (French) [Resurgent functions. Vol. I] Les alǵebres de fonctions ŕesurgentes. [The algebras of resurgent functions] With an English fore- word. Publications Math́ematiques d'Orsay 81 [Mathematical Publications of Orsay 81], 5, Universit́e de Paris-Sud, D́epartement de Math́ematique, Orsay, 1981, 247 pp.
3. V. Gelfreich and D. Sauzin, Borel summation and splitting ofseparatrices for the H́enon map, Ann. Inst. Fourier, Grenoble, 51 (2001), 513-567.
4. B. Malgrange, Resommation des śeries divergentes, (French) [Summation ofdivergent series], Exp. Math., 13 (1995), 163-222.
5. P. Martín, T. M. Seara and D. Sauzin, Exponentially small splitting of separatrices in per- turbations of the McMillan map, preprint, 2009.
6. C. Oliv́e, D. Sauzin and T. Seara, Resurgence in a Hamilton-Jacobi equation, Proceedings of the International Conference in Honor of Fŕed́eric Pham (Nice, 2002), Ann. Inst. Fourier, Grenoble, 53 (2003), 1185-1235.
7. D. Sauzin, Resurgentfunctions and splitting problems, RIMS Kokyuroku, 1493 (2005), 48-117.