On separatrix splitting of some quadratic area-preserving maps of the plane

Regular and Chaotic Dynamics

Volumn 3, Issue 1, 1998, Pages 49-65

  Chernov, V L ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54649084411     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1070/rd1998v003n01abeh000060     Document Type: Article

References (15)

1. V. G. Gelfreich, V. F. Lazutkin, M. B. Tabanov. Exponentially small splitting in hamiltonian systems // Chaos, 1991. Vol. 1, No 2, p. 137-142.
2. M. Hénon. Numerical study of quadratic area-preserving mappings // Quarterly of Applied Mathematics, 1969. Vol. 27, No 3, p. 291-312.
3. V. F. Lazutkin. Resurgent approach to the separatrices splitting // EQUADIFF 91. International Conference on Differential Equations. Vol. 1. Barcelona, Spain, August 26-31, 1991. Edited by C. Perelló, C.Simó, J. Solá-Morales. World Scientific, Singapore, New Jersey, London, Hong Kong 1993. P. 163-176.
4. J. Ecalle. Les fonctions résurgentes // Mathématiques d'Orsay 81-05. Tome 1: Les algébres de fonctions résurgentes.
5. V. L. Chernov. Resurgence of separatrices of the quadratic map // Universitat de Barcelona, November 1995. Mathematics Preprint Series, No 185, p. 13.
6. V. L. Chernov. Separatrix splitting for the Henon map: a resurgence approach // Universitat de Barcelona, November 1995. Mathematics Preprint Series, No 188, p. 17.
7. B. V. Chirikov. A universal instability of many-dimensional oscillators systems // Physics Reports, 1979. Vol. 52, p. 263-379.
8. A. I. Neishtadt. On the division of motions in the systems with fast rotating phase // Prikl. math, and mech., 1984. Vol. 48, No 2, p. 197-204 (Russian).
9. D. V. Treschev. The method of continuous averaging in the problem of separation of fast and slow motions // Regular and chaotic dynamics, 1997. Vol. 2, No 3/4, p. 9-20 (Russian).
10. A. J. Lichtenberg, M. A. Liberman. Regular and stochastic motion. New York-Heidelberg-Berlin: Springer-Verlag, 1983.
11. V. G. Gelfreich. Separatrix splitting for the polynomial area-preserving maps // Probl. math, phys., 1991. Vyp. 13. Editor Birman M. Sh. P. 108-116 (Russian).
12. V. F. Lazutkin. Exponential splitting of separatrices and an analytical integral for the semistandard map // Preprint, Université Paris VII, 1991. 53 p.;
13. An analytic integral along the separatrix of the semistandard map: existence and an exponential estimate for the distance between the stable and unstable separatrices // Algebra i Analis, 1992. Vol. 4, No 4, p. 110-142.
14. St.-Peterebuig Math. J., 1993. Vol. 4, No 4, p. 721-748.
15. N. Danford, J. T. Schwartz. Linear Operators, Part I: General theory. New York: Interscience publishers inc., 1958.