相关论文: Cascades of e-invisibility

The topological structure of basin boundaries plays a fundamental role in the sensitivity to the initial conditions in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum…

Selection of the preferred classical set of states in the process of decoherence -- so important for cosmological considerations -- is discussed with an emphasis on the role of information loss and entropy. {\it Persistence of correlations}…

We use the vacuum Bianchi I model as an example to investigate the concept of physical evolution in Loop Quantum Cosmology (LQC) in the absence of the massless scalar field which has been used so far in the literature as an internal time.…

We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive L\'{e}vy noise. The main result is applicable to various types of…

Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…

The aim of this paper is to study the finite-dimensional approximations of the nonautonomous lattice dynamical systems of the form $u_{i}'=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_{i}+F(u_i)+f_{i}(t)\ (i\in \mathbb Z)\ (*)$. We show that the…

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…

For bouncing cosmologies such as the ekpyrotic/cyclic scenarios we show that it is possible to make predictions for density perturbations which are independent of the details of the bouncing phase. This can be achieved, as in inflationary…

High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…

Let $\mathcal{R}$ be a strongly compact $C^2$ map defined in an open subset of an infinite-dimensional Banach space such that the image of its derivative $D_F \mathcal{R}$ is dense for every $F$. Let $\Omega$ be a compact, forward invariant…

Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…

High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…

This article is devoted to a study of the asymptotic dynamics of generic solutions of the Einstein vacuum equations toward a generic spacelike singularity. Starting from fundamental assumptions about the nature of generic spacelike…

We consider stochastic dynamics of lattice systems with finite local state space, possibly at low temperature, and possibly non-reversible. We assume the additional regularity properties on the dynamics: a) There is at least one stationary…

This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…

The East model is the simplest one-dimensional kinetically-constrained model of $N$ spins with a trivial equilibrium that displays anomalously large spatio-temporal fluctuations, with characteristic "space-time bubbles" in trajectory space,…

We present results on the non-linear dynamics of inhomogeneous cosmological models with irrotational dust and a positive cosmological constant, considering, in particular, a wide class with vanishing magnetic Weyl tensor. For those patches…