相关论文: Physical limit of prediction for chaotic motion of…

What is the origin of macroscopic randomness (uncertainty)? This is one of the most fundamental open questions for human being. In this paper, 10000 samples of reliable (convergent), multiple-scale (from 1.0E-60 to 100) numerical…

In this paper a new concept, namely the critical predictable time $T_c$, is introduced to give a more precise description of computed chaotic solutions of nonlinear differential equations: it is suggested that computed chaotic solutions are…

The famous three-body problem is investigated by means of a numerical approach with negligible numerical noises in a long enough time interval, namely the Clean Numerical Simulation (CNS). From physical viewpoints, position of any bodies…

Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…

The gravitational three-body problem is a rich open problem, dating back to Newton. It serves as a prototypical example of a chaotic system and has numerous applications in astrophysics. Generically, the motion is non-integrable and…

Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…

Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical…

We illustrate that, like the truncation error, the round-off error has a significant influence on the reliability of numerical simulations of chaotic dynamic systems. Due to the butterfly-effect, all numerical approaches in double precision…

We report a phenomenon that physical perturbations sometimes can benefit the certainty of a free-fall motion with chaotic modes, albeit, as commonly believed, they can ruin it. We statistically compare those factors that may lead to…

We find that localised perturbations in a chaotic classical many-body system-- the classical Heisenberg We find that the effects of a localised perturbation in a chaotic classical many-body system--the classical Heisenberg chain at infinite…

The mechanism responsible for the emergence of chaotic behavior has been identified analytically within a class of three-dimensional dynamical systems which generalize the well-known E.N. Lorenz 1963 system. The dynamics in the phase space…

The butterfly effect is today commonly identified with the sensitive dependence of deterministic chaotic systems upon initial conditions. However, this is only one facet of the notion of unpredictability pioneered by Lorenz, who actually…

The ``butterfly effect'', i.e. the growth of a localized infinitesimal perturbation, is the fundamental property of chaotic systems. While the butterfly effect is today an obvious property of low-dimensional chaotic systems, its…

The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…

The fundamental laws of physics are time-symmetric, but our macroscopic experience contradicts this. The time reversibility paradox is partly a consequence of the unpredictability of Newton's equations of motion. We measure the dependence…

The publication of Principia Mathematica in 1678 by Newton became known the celestial bodies motion laws, which characterize the Classical Mechanics. Thereafter made sense to search about the movement of these bodies from known initial…

Reliable prediction of large chaotic sytems in the short to middle time range is of interest in a number of fields, including climate, ecology, seismology, and economics. In this paper, results from chaos theory, and statistical theory are…

Linear equations with periodic coefficients describe the behavior of various dynamical systems. This studying is devoted to their applications to the planetary restricted three-body problem (RTBP). Here we consider the Laplace method for…

We study the chaotic dynamics in a classical many-body system of interacting spins on the kagome lattice. We characterise many-body chaos via the butterfly effect as captured by an appropriate out-of-time-ordered correlator. Due to the…