The weakly dissipative version of the Kolmogorov-Arnold-Moser theory and practical calculations |
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Authors: | R I Bogdanov M R Bogdanov |
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Institution: | (1) Skobeltsyn Institute of Nuclear Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia |
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Abstract: | 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. |
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Keywords: | Bogdanov-Takens bifurcation Bogdanov map Euler scheme adiabatic invariants Arnold diffusion treelike graph hierarchical structure periodic orbit |
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