Related papers: Time and Chaos in General Relativity
Defect-chaos is studied numerically in coupled Ginzburg-Landau equations for parametrically driven waves. The motion of the defects is traced in detail yielding their life-times, annihilation partners, and distances traveled. In a regime in…
We extend in several ways a recently proposed method to construct one-dimensional chaotic maps with exactly known natural invariant measure [Sogo 1999, 2009]. First, we assume that the given invariant measure depends on a continuous…
We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of…
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…
We outline the covariant nature of the chaos characterizing the generic cosmological solution near the initial singularity. Our analysis is based on a "gauge" independent ADM-reduction of the dynamics to the physical degrees of freedom, and…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…
The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fr\'{e}chet space. The other is about…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
The Mixmaster or Bianchi IX cosmological model has become one of the archetypal settings for studying gravitational dynamics. The past decade has seen a vigourous debate about whether or not the Mixmaster's dynamics is chaotic. In this talk…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
This paper tackles Hamiltonian chaos by means of elementary tools of Riemannian geometry. More precisely, a Hamiltonian flow is identified with a geodesic flow on configuration space-time endowed with a suitable metric due to Eisenhart.…
Within random matrix theory, the statistics of the eigensolutions depend fundamentally on the presence (or absence) of time reversal symmetry. Accepting the Bohigas-Giannoni-Schmit conjecture, this statement extends to quantum systems with…
Is it possible to define what we could mean by chaos in a space-time metric (even in the simplest toy-model studies)? Is it of importance for phenomena we may search for in Nature?
A particular example of chaos can be conceived in the interaction of non-linear oscillator with a harmonic gravitational wave. When we replace the linear potential forces by the therm SIN(x), the type of solution becomes subject to external…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the…
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to…
While extensive research has been conducted on chaos emerging from a dynamical system's temporal dynamics, our research examines extreme sensitivity to initial conditions in discrete-time dynamical systems from a geometrical perspective.…
We investigate the role of quantum monitoring in the dynamical manifestations of Hamiltonian quantum chaos. Specifically, we analyze the generalized spectral form factor, defined as the survival probability of a coherent Gibbs state under…
In recent years there has been a lot of interest in discussing frame dependences/independences of the cosmological perturbations under the conformal transformations. This problem has previously been investigated in terms of the covariant…