The weakly dissipative version of the Kolmogorov–Arnold–Moser theory and practical calculations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 473-490
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The weakly dissipative version of the Kolmogorov–Arnold–Moser theory deals with the dynamics of systems that are a weakly dissipative perturbation of Hamiltonian systems. In the framework of this approach, both regular (asymptotically stable (unstable) periodic motions) and stochastic (Arnold's web) dynamic properties are combined in the phase space. In this case, computer calculations are considerably simplified for the regular dynamics, which makes it possible to estimate physical parameters for stochastic components. A simple example of this approach is presented.
@article{ZVMMF_2008_48_3_a8,
author = {R. I. Bogdanov and M. R. Bogdanov},
title = {The weakly dissipative version of the {Kolmogorov{\textendash}Arnold{\textendash}Moser} theory and practical calculations},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {473--490},
publisher = {mathdoc},
volume = {48},
number = {3},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a8/}
}
TY - JOUR AU - R. I. Bogdanov AU - M. R. Bogdanov TI - The weakly dissipative version of the Kolmogorov–Arnold–Moser theory and practical calculations JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2008 SP - 473 EP - 490 VL - 48 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a8/ LA - ru ID - ZVMMF_2008_48_3_a8 ER -
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R. I. Bogdanov; M. R. Bogdanov. The weakly dissipative version of the Kolmogorov–Arnold–Moser theory and practical calculations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 473-490. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a8/