Continuous averaging in multi-frequency slow-fast systems

Regular and Chaotic Dynamics

Volumn 5, Issue 2, 2000, Pages 157-170

  Pronin, A V ^a   Treschev, D V ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0344303405     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1070/RD2000v005n02ABEH000138     Document Type: Article

References (18)

1. V. Arnold. Instability of Dynamical Systems with Several Degrees of Freedom, Dokl. Akad. Nauk SSSR, 1964, V. 156, No 1, P. 9-12,
2. English transl. in Sov. Mat. Dokl., 1964, V. 5, P. 581-585.
3. D. Bambusi. Long Time Stability of Some Small Amplitude Solutions in Nonlinear Schrödinger Equations. Comm. Math. Phys., 1997, V. 189, P. 205-226.
4. A. Delshams, V. Gelfreich, A. Jorba, T. Seara. Exponentially Small Splitting of Separatrices Under Fast Quasi-Periodic Forcing. Comm. Math. Phys., 189, 1997, P. 35-71.
5. A. Delshams, D. Gutiérres. Splitting Potential and Poincare-Melnikov Theory for Whiskered Tori in Hamiltonian Systems. Preprint, 1998. http://www-mal.upc.es
6. A. Delshams, T. Seara. An Asymptotic Expression for the Splitting of Separatrices of the Rapidly Forced Pendulum, Comm. Math. Phys., 150, 1992, P. 433-463.
7. G. Gallavotti. Twistless KAM Tori, Quasi-Flat Homoclinic Intersections, and Other Cancellations in the Perturbation Series of Certain Completely Integrable Systems. A review, Reviews in Mathematical Physics, 6, 1994, P. 343-411.
8. V. Gelfreich. Reference Systems for Splitting of Separatrices. Nonlinearity, V. 10, 1997, P. 175-193.
9. V. Gelfreich. A Proof of the Exponentially Small Transversality of the Separatrices for the Standard Map. Comm. Math. Phys., V. 201, 1999.
10. V. Lazutkin. Splitting of Separatrices for Standard Chirikov's Mapping. VINITI, No6372-84, 24 Sept., 1984. (in Russian)
11. A. Neishtadt. The Separation of Motions in Systems with Rapidly Rotating Phase. Prikl. Mat. Mekh., 1984, V. 48, No 2, P. 197-204. (in Russian)
12. English transl. in J. Appl. Math. Mech., 1984, V. 48, No 2, P. 133-139.
13. J. P. Ramis, R. Schäfke. Gevrey Separation of Fast and Slow Variables. Nonlinearity, V. 9, 1996, P. 353-384.
14. D. Sauzin. A New Method for Measuring the Splitting of Invariant Manifolds. 1999, Notes Scientifiques et Techniques du Bureau des Longitudes.
15. C. Simó. Averaging Under Fast Quasi-Periodic Forcing in Hamiltonian Mechanics: Integrability and Chaotic Behavior. J. Seimenis ed., NATO Adv. Sci. Inst. Ser. B Phys., 331, Plenum Press, New York 1994, P. 13-34.
16. D. Treschev. Separatrix Splitting for a Pendulum with Rapidly Oscillating Suspension Point. Russian J. of Math. Phys., 1997, V. 5, No. 1, P. 63-98.
17. D. Treschev. An Averaging Method for Hamiltonian Systems, Exponentially Close to Integrable Ones. Chaos, V.6, No. 1, 1996, P. 6-14.
18. D. Treschev. The Continuous Averaging Method in the Problem of Separation of Fast and Slow Motions. Regular and Chaotic Dynamics, V. 2, No 3/4, 1997, P. 9-20. (In Russian)