Related papers: Trajectory arclength reveals chaos
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
Randomization of the Lagrangian chaos in fluid dynamics has been analyzed using results of direct numerical simulations, laboratory measurements, and oceanic observations. The notion of distributed chaos has been used in order to quantify…
Thermodynamics is independent of a description at a microscopic level consequently statistical thermodynamics must produce results independent of the coordinate system used to describe the particles and their interactions. In the path…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
The use of statistical methods for the description of complex quantum systems was primarily motivated by the failure of a line-by-line interpretation of atomic spectra. Such methods reveal regularities and trends in the distributions of…
In this paper we analyze the transport of passive tracers by deterministic stationary incompressible flows which can be decomposed over an infinite number of spatial scales without separation between them. It appears that a low order…
A method for extracting time-varying oscillatory motions from time series records is applied to Lagrangian trajectories from a numerical model of eddies generated by an unstable equivalent barotropic jet on a beta plane. An oscillation in a…
I prove a theorem on the precise connection of the time and phase space average of the Boltzmann equilibrium showing that the behaviour of a dynamical system with a stationary measure and a dominant equilibrium state is qualitatively…
We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and derive a classical sum…
Chaotic systems are characterised by exponential separation between close-by trajectories, which in particular leads to deterministic unpredictability over an infinite time-window. It is now believed, that such butterfly effect is not fully…
Given an arbitrary \(V \times V\) Hermitian matrix, considered as a finite discrete quantum Hamiltonian, we use methods from graph and ergodic theories to construct a \textit{quantum Poincar\'e map} at energy \(E\) and a corresponding…
The escape dynamics around the triangular Lagrangian point L5 in the real Sun-Earth-Moon-Spacecraft system is investigated. Appearance of the finite time chaotic behaviour suggests that widely used methods and concepts of dynamical system…
Lagrangian stochastic models are widely used to predict and analyze turbulent dispersion in complex environments, such as in various terrestrial and marine canopy flows. However, due to a lack of empirical data, it is still not understood…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
From the integer quantum Hall effect, to swimming at low Reynolds number, geometric phases arise in the description of many different physical systems. In many of these systems the temporal evolution prescribed by the geometric phase can be…
Here, we introduce a novel method for obtaining chaotic dynamics based on the Montgomery conjecture for the pair correlation of zeros of the Riemann zeta function. Motivated by the conjecture, we present a recursive relation that reveals…
Developing measures of quantum ergodicity and chaos stands as a foundational task in the study of quantum many-body systems. In this work, we propose metrics for these effects based on Hamiltonian learning that unify multiple advantages of…
The route to chaos and phase dynamics in a rotating shallow-water model were rigorously examined using a five-mode Galerkin truncated system with complex variables. This system is valuable for investigating how large/meso-scales destabilize…
We analyze the properties of the self-similar network obtained from the trajectories of unimodal maps at the transition to chaos via the horizontal visibility (HV) algorithm. We first show that this network is uniquely determined by the…
The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure $\psi(\beta)$. The inverse-temperature like variable $\beta$ allows one to scan the structure of the probability distribution in…