Related papers: Proximality, stability, and central limit theorem …
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
For non uniformly hyperbolic maps of the interval with exponential decay of correlations we prove that the law of closest return to a given point when suitably normalized is almost surely asymptotically exponential. A similar result holds…
Non-linear maps can possess various dynamical behaviors varying from stable steady states and cycles to chaotic oscillations. Most models assume that individuals within a given population are identical ignoring the fundamental role of…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
We consider a non-nestling random walk in a product random environment. We assume an exponential moment for the step of the walk, uniformly in the environment. We prove an invariance principle (functional central limit theorem) under almost…
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…
We continue development of the theory of Markov systems initiated in \cite{Wer1}. In this paper, we introduce fundamental Markov systems associated with random dynamical systems and show that the proof of the uniqueness and empiricalness of…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
We briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations and with existing central limit theorems. We then provide some hints that might pave the road to the proof of…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
Employing model predictive control to systems with unbounded, stochastic disturbances poses the challenge of guaranteeing safety, i.e., repeated feasibility and stability of the closed-loop system. Especially, there are no strict repeated…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
Suppose we can choose from a set of linear autonomous systems with bounded process noise, the dynamics of each system are unknown, and we would like to design a stabilizing policy. The underlying question is how to estimate the dynamics of…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
We introduce the {\em $\mu$-topological stability}. This is a type of stability depending on the measure $\mu$ different from the set-valued approach \cite{lm}. We prove that the map $f$ is $m_p$-topologically stable if and only if $p$ is a…
In this paper we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles…