On the recurrence and Lyapunov time scales of the motion near the chaos border

Abstract

Conditions for the emergence of a statistical relationship between $T_r$, the chaotic transport (recurrence) time, and $T_L$, the local Lyapunov time (the inverse of the numerically measured largest Lyapunov characteristic exponent), are considered for the motion inside the chaotic layer around the separatrix of a nonlinear resonance. When numerical values of the Lyapunov exponents are measured on a time interval not greater than $T_r$, the relationship is shown to resemble the quadratic one. This tentatively explains numerical results presented in the literature.

16 pages, 2 figures

Cited by in corpus (9)

• Lyapunov exponents in resonance multiplets
• The Kepler map in the three-body problem
• The Stability Boundary of the Distant Scattered Disk
• On the maximum Lyapunov exponent of the motion in a chaotic layer
• Isles of regularity in a sea of chaos amid the gravitational three-body problem
• Isentropic perturbations of a chaotic domain
• Lyapunov exponents in fundamental models of nonlinear resonance
• Massive evaluation and analysis of Poincaré recurrences on grids of initial data: a tool to map chaotic diffusion
• Recent arrivals to the main asteroid belt