53 citations · 644 across the 34 of their papers we have counts for
9 papers · 1 filter
Massive evaluation and analysis of Poincaré recurrences on grids of initial data: a tool to map chaotic diffusion
Ivan I. Shevchenko, Guillaume Rollin, Alexander V. Melnikov +1
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincaré recurr…
Marginal resonances and intermittent behaviour in the motion in the vicinity of a separatrix
Ivan I. Shevchenko
A condition upon which sporadic bursts (intermittent behaviour) of the relative energy become possible is derived for the motion in the chaotic layer around the separatrix of non-l…
On the recurrence and Lyapunov time scales of the motion near the chaos border
Ivan I. Shevchenko
Conditions for the emergence of a statistical relationship between , the chaotic transport (recurrence) time, and , the local Lyapunov time (the inverse of the numericall…
Isentropic perturbations of a chaotic domain
I. I. Shevchenko
Three major properties of the chaotic dynamics of the standard map, namely, the measure μof the main connected chaotic domain, the maximum Lyapunov exponent L of the motion in this…
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…