`a`
Electronic Research Announcements in Mathematical Sciences (ERA-MS)
 

Special functions created by Borel-Laplace transform of Hénon map
Pages: 1 - 11, January 2011

doi:10.3934/era.2011.18.1      Abstract        References        Full text (670.0K)           Related Articles

Chihiro Matsuoka - Department of Physics, Graduate school of Science and Technology, Ehime University, Bunkyocho 2-5, Matsuyama 790-8577, Japan (email)
Koichi Hiraide - Department of Mathematics, Graduate school of Science and Technology, Ehime University, Bunkyocho 2-5, Matsuyama 790-8577, Japan (email)

1 M. Hénon, A two-dimensional mapping with a strange attractor, Commun. Math. Phys., 50 (1976), 69-77.       
2 E. N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci., 20 (1963), 130-141.
3 V. Hakim and K. Mallick, Exponentially small splitting of separatrices, matching in the complex plane and Borel summation, Nonlinearity, 6 (1993), 57-70.       
4 A. Tovbis, Asymptotics beyond all orders and analytic properties of inverse Laplace trnsforms of solutions, Commun. Math. Phys., 163 (1994), 245-255.       
5 A. Tobvis, M. Tsuchiya and C. Jaffe, Exponential asymptotic expansions and approximations of the unstable and stable manifolds of singularly perturbed systems with the Hénon map as an example, Chaos, 8 (1998), 665-681.       
6 K. Nakamura and M. Hamada, Asymptotic expansion of homoclinic structures in a symplectic mapping, J. Phys. A, 29 (1996), 7315-7327.       
7 V. F. Lazutkin, I. G. Schachmannski and M. B. Tabanov, Splitting of separatrices for standard and semistandard mappings, Physica D, 40 (1989), 235-248.       
8 M. D. Kruskal and H. Segur, Asymptotics beyond all orders in a model of crystal growth, Stud. Appl. math., 85 (1991), 129-181.       
9 H. Segur, S. Tanveer and H. Levine (eds), "Asymptotics Beyond All Orders," (Plenum, New York), 1991.
10 A. Voros, The return of quartic oscillator: The complex WKB method, Ann. Inst. H. Poincaré 39 (1983), 211-338.       
11 J. Écalle, "Les Fonctions Résurgence vol. 1," (French) [Resurgent functions. Vol. I] Les algèbres de fonctions résurgentes. [The algebras of resurgent functions] With an English foreword. Publications Mathématiques d'Orsay 81 [Mathematical Publications of Orsay 81], 5. Université de Paris-Sud, Département de Mathématique, Orsay, 1981.       
12 J. Écalle, "Les Fonctions Résurgence vol. 2," (French) [Resurgent functions. Vol. II] Les fonctions résurgentes appliquées à l'itération. [Resurgent functions applied to iteration] Publications Mathématiques d'Orsay 81 [Mathematical Publications of Orsay 81], 6. Université de Paris-Sud, Département de Mathématique, Orsay, 1981.       
13 J. Écalle, "Les Fonctions Résurgence vol. 3," (French) [Resurgent functions. Vol. III] L' équation du pont et la classification analytique des objects locaux. [The bridge equation and analytic classification of local objects] Publications Mathématiques d'Orsay [Mathematical Publications of Orsay], 85-5. Université de Paris-Sud, Département de Math¨¦matiques, Orsay, 1985.       
14 B. Y. Sternin and V. E. Shatalov, "Borel-Laplace Transform and Asymptotic Theory," Introduction to Resurgent Analysis, CRC Press, Boca Raton, FL, 1996.
15 V. Gelfreich and D. Sauzin, Borel summation and splitting of separatrices for the Hénon map, Ann. Inst. Fourier (Grenoble), 51 (2001), 513-67.       
16 S. Newhouse and T. Pignataro, On the estimation of topological entropy, J. Stat. Phys., 72 (1993), 1331-1351.       

Go to top