Related papers: Stochastic Shadowing and Stochastic Stability

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain…

We provide a new approach to stable ergodicity of systems with dominated splittings, based on a geometrical analysis of global stable and unstable manifolds of hyperbolic points. Our method suggests that the lack of uniform size of Pesin's…

We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along…

In this note we study some properties of topological entropy for noncompact non-metrizable spaces.

We obtain a characterization of two classes of dynamics with nonuniformly hyperbolic behavior in terms of an admissibility property. Namely, we consider exponential dichotomies with respect to a sequence of norms and nonuniformly hyperbolic…

We investigate a shadowing property which appears naturally in the study of piecewise monotonic maps of the interval. It turns out to be a weak form of the rank one property, a well-known notion in abstract ergodic theory. We show that this…

This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…

Predictability horizon properties of chaotic dynamical systems can be related to their spectral properties. It is shown, using this relationship, that the spectral properties of the leading large-scale climate daily indices indicate a…

Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combination, minimum contrast estimators are introduced. Strong…

In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map $f$ of a uniform space has topological shadowing property then the map $f$ has positive…

The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just…

Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…

The purpose of this work is threefold: (i) extend shadowing theory for discontinuous and non-invertible systems, (ii) consider more general classes of perturbations (for example, small only on average), (iii) establish a general theory…

A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…

Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…

This article is about the shadowing property of homeomorphisms on compact metric spaces and the map associating a point of the space to each pseudo-orbit, called 'shadowing map'. Based on some particular dynamical properties, as…

We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…

In this paper we present a systematic study of shadowing properties with average error in tracing such as (asymptotic) average shadowing, $\underline{d}$-shadowing, $\overline{d}$-shadowing and almost specification. As the main tools we…

A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation…

Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…