The regular dynamics through the finite‐time Lyapunov exponent distributions in 3D Hamiltonian systems

Abstract

AbstractWe investigate the application as a technique of the so‐called finite‐time Lyapunov exponent, a scalar value that measures the average, or integrated, separation between trajectories in integrable dynamical systems to quantify the predictability limit of the asymptotic global behavior of old compact star systems (1–10 Gyr), for instance, neutron stars. For this purpose, the Hamiltonian systems with a three‐dimensional self‐gravitating axisymmetric potential are superimposed due to the influence of different birth and kick velocity distributions. We find the behavior of the density distributions P(x) for the finite‐time exponents, which follow a log‐normal distribution (transformed into a Gaussian distribution), with a given mean deviation centered around the global values, at larger Δt. It is shown that simple models of distributions reflect the underlying dynamics. We also analyze the predictability and the deviation vector ω(t), obtained from the distributions, by randomly selecting the initial deviation directions, and consequently the stellar dynamic stability of the periodic orbits, in three‐dimensional (3D) Hamiltonian systems over time. The behavior of the orbits is strongly influenced by the regular nature of the motion.