相关论文: Covariant Mixmaster Dynamics

We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…

We study the long time statistics of a two-dimensional Hamiltonian system in the presence of Gaussian white noise. While the original dynamics is known to exhibit finite time explosion, we demonstrate that under the impact of the stochastic…

Using the existence of a covariant conserved quantity on large perturbation scales in a spatially flat perfect fluid or scalar field universe, we present a general formula for gauge-invariantly defined comoving energy density perturbations…

Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated…

The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…

An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to…

This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…

A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…

Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and…

In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so called covariant perturbations. It is often argued in the literature that one…

We investigate the dependence of Poincar\'e recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct…

Hamilton-Jacobi theory provides a natural starting point for a covariant description of the gravitational field. Using a spatial gradient expansion, one may solve for the phase of the wavefunction by using a line-integral in superspace.…

The dynamical systems invariant under gauge transformations with higher order time derivatives of the gauge parameter are considered from the Hamiltonian point of view. We investigate the consequences of the basic requirements that the…

A novel expansion -- which generalizes Magnus expansion -- of the evolution operator associated with a (in general, time-dependent) perturbed Hamiltonian is introduced. It is shown that it has a wide range of possible solutions that can be…

It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…

We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…

We consider the classical and quantum dynamics in M(atrix) theory. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. We argue that the holographic feature of M(atrix) theory is related with the repulsive…

In this paper we present a theoretical analysis of the global dynamics in a triaxial galactic system using a 3D integrable Hamiltonian as a simple representation. We include a thorough discussion on the effect of adding a generic…

We consider cosmological models with a scalar field with equation of state $w\ge 1$ that contract towards a big crunch singularity, as in recent cyclic and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to anisotropy…

Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as…