Related papers: Screen chaotic motion by Shannon entropy in curved…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…
Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in…
Using the tools of Differential Geometry, we define a new <<fast>> chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e. "quickly") than the usual tools, like Lyapunov Characteristic Numbers…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
Recent work by Shenker, Stanford, and Kitaev has related the black hole horizon geometry to chaotic behavior. We extend this from eternal black holes to black holes that form and then evaporate. This leads to an identity for the change in…
In this paper, we use Lyapunov exponents to analyze how the dynamical properties of the H\'enon map change as a function of the coefficients of a linear filter inserted in its feedback loop. We show that the generated orbits can be chaotic…
This paper investigates chaos and chaotic phase mixing in triaxial Dehnen potentials which have been proposed to describe realistic ellipticals. Earlier work is extended by exploring the effects of (1) variable axis ratios, (2) `graininess'…
Via evaluation of the Lyapunov exponent, we report the discovery of three prominent sets of phase space regimes of quasi-periodic orbits of charged particles trapped in a dipole magnetic field. Besides the low energy regime that has been…
Classical motion of positronium embedded in a magnetic field is studied, and computation shows the emergence of chaotic orbits. Recent work investigating quantum behavior of this system predicts extremely long lifetimes. Chaos assisted…
Shannon entropy in position ($S_{\rvec}$) and momentum ($S_{\pvec}$) spaces, along with their sum ($S_t$) are presented for unit-normalized densities of He, Li$^+$ and Be$^{2+}$ ions, spatially confined at the center of an impenetrable…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass…
This paper discusses applications of a particular control technique that can be used to very efficiently stabilize a chaotic system onto a large subset of the unstable periodic orbits that are typically embedded in the system. The control…
We study behaviour of ionized region of a Keplerian disk orbiting a Schwarzschild black hole immersed in an asymptotically uniform magnetic field. In dependence on the magnetic parameter ${\cal B}$, and inclination angle $\theta$ of the…
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…
While plenty of results have been obtained for single-particle quantum systems with chaotic dynamics through a semiclassical theory, much less is known about quantum chaos in the many-body setting. We contribute to recent efforts to make a…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…
The existing periodic orbit theory of spectral correlations for classically chaotic systems relies on the Riemann-Siegel-like representation of the spectral determinants which is still largely hypothetical. We suggest a simpler derivation…