Related papers: Revisit on "Ruling out chaos in compact binary sys…
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of…
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…
The ability of the Smaller Alignment Index (SALI) to distinguish chaotic from ordered motion, has been demonstrated recently in several publications.\cite{Sk01,GRACM} Basically it is observed that in chaotic regions the SALI goes to zero…
We show, using covariant Lyapunov vectors in addition to standard Lyapunov analysis, that there exists a set of collective Lyapunov modes in large chaotic systems exhibiting collective dynamics. Associated with delocalized Lyapunov vectors,…
New computational technique based on the symbolic description utilizing kneading invariants is used for explorations of parametric chaos in a two exemplary systems with the Lorenz attractor: a normal model from mathematics, and a laser…
We derive a criterion for the onset of chaos in systems consisting of two massive, eccentric, coplanar planets. Given the planets' masses and separation, the criterion predicts the critical eccentricity above which chaos is triggered. Chaos…
Binary black holes in which both spins are aligned with the binary's orbital angular momentum do not precess. However, the up-down configuration, in which the spin of the heavier (lighter) black hole is aligned (anti-aligned) with the…
We calculate the explicit equations of motion for non-spinning compact objects to 2.5 post-Newtonian order, or O(v/c)^5 beyond Newtonian gravity, in a general class of scalar-tensor theories of gravity. We use the formalism of the Direct…
The relativistic motion of a compact binary system moving in circular orbit is investigated using the post-Newtonian (PN) approximation and the perturbative self-force (SF) formalism. A particular gauge-invariant observable quantity is…
Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…
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…
Conley in \cite{Con} constructed a complete Lyapunov function for a flow on compact metric space which is constant on orbits in the chain recurrent set and is strictly decreasing on orbits outside the chain recurrent set. This indicates…
Globally coupled maps (GCMs) are prototypical examples of high-dimensional dynamical systems. Interestingly, GCMs formed by an ensemble of weakly coupled identical chaotic units generically exhibit a hyperchaotic 'turbulent' state. A decade…
We report a dynamical phase transition from integrability to non-integrability in a simple oval-like billiard with boundary $R(\theta)=1+\epsilon\cos(p\theta)$. For $\epsilon=0$, the phase space is {\it foliated} by invariant curves…
Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of…
The recent gravitational wave observations by the LIGO/Virgo collaboration have allowed the first tests of General Relativity in the extreme gravity regime, when comparable-mass black holes and neutron stars collide. Future space-based…
Do nonlinear waves destroy Anderson localization? Computational and experimental studies yield subdiffusive nonequilibrium wave packet spreading. Chaotic dynamics and phase decoherence assumptions are used for explaining the data. We…
This article tackles a fundamental long-standing problem in quantum chaos, namely, whether quantum chaotic systems can exhibit sensitivity to initial conditions, in a form that directly generalizes the notion of classical chaos in phase…
The dynamical instability of rough hard-disk fluids in two dimensions is characterized through the Lyapunov spectrum and the Kolmogorov-Sinai entropy, $h_{KS}$, for a wide range of densities and moments of inertia $I$. For small $I$ the…
We consider a generalisation of Ulam's method for approximating invariant densities of one-dimensional chaotic maps. Rather than use piecewise constant polynomials to approximate the density, we use polynomials of degree n which are defined…