Geodesic
On exponentially small effects in dynamical systems with a small parameter
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 273-278 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the present paper we obtain a theorem which enables us to treat different exponentially small effects of dynamics from a unified point of view. As an example, we discuss the problem of fast phase averaging in non-autonomous Hamiltonian system with 3/2 degrees of freedom. 
@article{ZNSL_2003_300_a28,
     author = {O. \`E. Zubelevich},
     title = {On exponentially small effects in dynamical systems with a~small parameter},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {273--278},
     year = {2003},
     volume = {300},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a28/}
}
TY  - JOUR
AU  - O. È. Zubelevich
TI  - On exponentially small effects in dynamical systems with a small parameter
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 273
EP  - 278
VL  - 300
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a28/
LA  - en
ID  - ZNSL_2003_300_a28
ER  - 
%0 Journal Article
%A O. È. Zubelevich
%T On exponentially small effects in dynamical systems with a small parameter
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 273-278
%V 300
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a28/
%G en
%F ZNSL_2003_300_a28
O. È. Zubelevich. On exponentially small effects in dynamical systems with a small parameter. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 273-278. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a28/

[1] C. Bonnet, D. Sauzin, T. Seara, M. Valencia, “Adiabatic invariant of the harmonic oscillator, complex matching resurgence”, SIAM J. Math. Anal., 29:6 (1998), 1335–1360 | DOI | MR

[2] J. Appl. Math. Mech., 48:2 (1984), 133–139 | DOI | MR

[3] A. Pronin, D. Treschev, “Continuous averaging in multi-frequency slow-fast systems”, Regular and Chaotic Dynamics, 5:2 (2000), 157–170 | DOI | MR | Zbl

[4] C. Simó, “Averaging under fast quasi-periodic forcing in Hamiltonian mechanics: Integrability and chaotic behavior”, NATO Adv. Sci. Inst. Ser. B Phys., 331, ed. J. Seimenis, Plenum Press, New York, 1994, 13–34 | MR

[5] Slitskin A. A., “On the motion of one-dimensional oscillator under adiabatic conditions”, Zhurn. Exper. Teor. Fiz., 45:4 (1963), 978–988