Related papers: Invariant scrambled sets, uniform rigidity and wea…
We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals.…
In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a countable set. More specifically, we show…
We consider the collection of uniformly discrete point sets in Euclidean space equipped with the vague topology. For a point set in this collection, we characterise minimality of an associated dynamical system by almost repetitivity of the…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
The stability of the system is an important part of the research on differential dynamical systems. This paper considers a pointwise hyperbolic system defined on a connected open subset N of a compact smooth Riemannian manifold M. The…
For a dynamical system $(X,f)$, $X$ being a compact metric space with metric $d$ and $f$ being a continuous map $X\to X$, a set $S\subseteq X$ is scrambled if every pair $(x,y)$ of distinct points in $S$ is scrambled, i.e.,…
In present paper we mainly focus on non-recurrent dynamical orbits with empty syndetic center and show that twelve different statistical structures over mixing expanding maps or transitive Anosov diffeomorphisms all have dynamical…
We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…
We numerically investigate the properties of speckle patterns formed by nonlinear point scatterers. We show that, in the weak localization regime, dynamical instability appears, eventually leading to chaotic behavior of the system.…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…
We study the statics and dynamics of an elastic manifold in a disordered medium with quenched defects correlated as r^{-a} for large separation r. We derive the functional renormalization-group equations to one-loop order, which allow us to…
We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…
We consider a class of doubly intermittent maps with critical points, unbounded derivative and regularly varying tails. Under some mild assumptions we prove the existence of a unique mixing absolutely continuous invariant measure and give…
We introduce conformal mixed finite element methods for $2$D and $3$D incompressible nonlinear elasticity in terms of displacement, displacement gradient, the first Piola-Kirchhoff stress tensor, and pressure, where finite elements for the…
This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…
In the following text, for finite discrete $X$ with at least two elements, nonempty countable $\Gamma$, and $\varphi:\Gamma\to\Gamma$ we prove the generalized shift dynamical system $(X^\Gamma,\sigma_\varphi)$ is densely chaotic if and only…
It is well known that \omega-limit sets are internally chain transitive and have weak incompressibility; the converse is not generally true, in either case. However, it has been shown that a set is weakly incompressible if and only if it is…
The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\times f^2 \times...\times f^m$, where $f\colon X\ra X$ is a topological dynamical system on a…
We introduce a new class of mixed finite element methods for 2D and 3D compressible nonlinear elasticity. The independent unknowns of these conformal methods are displacement, displacement gradient, and the first Piola-Kirchhoff stress…