53 citations · 644 across the 34 of their papers we have counts for
8 papers · 1 filter
Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points
I. I. Shevchenko
The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of au…
The width of a chaotic layer
Ivan I. Shevchenko
A model of nonlinear resonance as a periodically perturbed pendulum is considered, and a new method of analytical estimating the width of a chaotic layer near the separatrices of t…
The Kepler map in the three-body problem
Ivan I. Shevchenko
The Kepler map was derived by Petrosky (1986) and Chirikov and Vecheslavov (1986) as a tool for description of the long-term chaotic orbital behaviour of the comets in nearly parab…
The dynamical temperature and the standard map
I. I. Shevchenko
Numerical experiments with the standard map at high values of the stochasticity parameter reveal the existence of simple analytical relations connecting the volume and the dynamica…
Width of the chaotic layer: maxima due to marginal resonances
Ivan I. Shevchenko
Modern theoretical methods for estimating the width of the chaotic layer in presence of prominent marginal resonances are considered in the perturbed pendulum model of nonlinear re…
Lyapunov exponents in resonance multiplets
I. I. Shevchenko
The problem of estimating the maximum Lyapunov exponents of the motion in a multiplet of interacting nonlinear resonances is considered for the case when the resonances have compar…