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Special functions created by Borel-Laplace transform of Hénon map
1. | Department of Physics, Graduate school of Science and Technology, Ehime University, Bunkyocho 2-5, Matsuyama 790-8577, Japan |
2. | Department of Mathematics, Graduate school of Science and Technology, Ehime University, Bunkyocho 2-5, Matsuyama 790-8577, Japan |
References:
[1] |
M. Hénon, A two-dimensional mapping with a strange attractor, Commun. Math. Phys., 50 (1976), 69-77.
doi: doi:10.1007/BF01608556. |
[2] |
E. N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci., 20 (1963), 130-141.
doi: doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2. |
[3] |
V. Hakim and K. Mallick, Exponentially small splitting of separatrices, matching in the complex plane and Borel summation, Nonlinearity, 6 (1993), 57-70.
doi: doi:10.1088/0951-7715/6/1/004. |
[4] |
A. Tovbis, Asymptotics beyond all orders and analytic properties of inverse Laplace trnsforms of solutions, Commun. Math. Phys., 163 (1994), 245-255.
doi: doi:10.1007/BF02102008. |
[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.
doi: doi:10.1063/1.166349. |
[6] |
K. Nakamura and M. Hamada, Asymptotic expansion of homoclinic structures in a symplectic mapping, J. Phys. A, 29 (1996), 7315-7327.
doi: 10.1088/0305-4470/29/22/025. |
[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.
doi: doi:10.1016/0167-2789(89)90065-1. |
[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. |
show all references
References:
[1] |
M. Hénon, A two-dimensional mapping with a strange attractor, Commun. Math. Phys., 50 (1976), 69-77.
doi: doi:10.1007/BF01608556. |
[2] |
E. N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci., 20 (1963), 130-141.
doi: doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2. |
[3] |
V. Hakim and K. Mallick, Exponentially small splitting of separatrices, matching in the complex plane and Borel summation, Nonlinearity, 6 (1993), 57-70.
doi: doi:10.1088/0951-7715/6/1/004. |
[4] |
A. Tovbis, Asymptotics beyond all orders and analytic properties of inverse Laplace trnsforms of solutions, Commun. Math. Phys., 163 (1994), 245-255.
doi: doi:10.1007/BF02102008. |
[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.
doi: doi:10.1063/1.166349. |
[6] |
K. Nakamura and M. Hamada, Asymptotic expansion of homoclinic structures in a symplectic mapping, J. Phys. A, 29 (1996), 7315-7327.
doi: 10.1088/0305-4470/29/22/025. |
[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.
doi: doi:10.1016/0167-2789(89)90065-1. |
[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. |
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