Related papers: Specification properties on uniform spaces

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified…

We consider some general classes of random dynamical systems and show that a priori very weak nonuniform hyperbolicity conditions actually imply uniform hyperbolicity.

It is shown how to model any automorphism of a totally disconnected, locally compact group by a symbolic dynamical system. The model is an inverse limit of a product of a full-shift, on a finite number of symbols, with one of two types of…

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…

We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate for this class of spaces, that in…

This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…

Let $(X, \Gamma)$ be a free and minimal topological dynamical system, where $X$ is a separable compact Hausdorff space and $\Gamma$ is a countable infinite discrete amenable group. It is shown that if $(X, \Gamma)$ has the Uniform Rokhlin…

Let $(X,G,\Phi)$ be a dynamical system, where $X$ is compact Hausdorff space, and $G$ is a countable discrete group. We investigate shadowing property and mixing between subshifts and general dynamical systems. For the shadowing property,…

We consider a general class of nonlinear, constrained, discrete-time systems whose dynamics are parametrized by a set of gains. We define the semiglobal, practical, asymptotic stability (SPAS) of compact sets for this class of systems, and…

We obtain large deviation bounds for the measure of deviation sets associated to asymptotically additive and sub-additive potentials under some weak specification properties. In particular a large deviation principle is obtained in the case…

We study expansive dynamical systems from the viewpoint of general topology. We introduce the notions of orbit and refinement expansivity on topological spaces extending expansivity in the compact metric setting. Examples are given on…

We discuss definable compactifications and topological dynamics. For G a group definable in some structure M, we define notions of "definable" compactification of G and "definable" action of G on a compact space X (definable G-flow), where…

The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via…

We investigate some ergodic and spectral properties of general (discrete) $C^*$-dynamical systems $({\mathfrak A},\Phi)$ made of a unital $C^*$-algebra and a multiplicative, identity-preserving $*$-map $\Phi:{\mathfrak A}\to{\mathfrak A}$,…

For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…

We study the low temperature dynamics of a two dimensional short-range spin system with uniform ferromagnetic interactions, which displays glassiness at low temperatures despite the absence of disorder or frustration. The model has a dual…

We develop the dichotomy spectrum for random dynamical system and demonstrate its use in the characterization of pitchfork bifurcations for random dynamical systems with additive noise. Crauel and Flandoli had shown earlier that adding…

We demonstrate with a minimal example that in Filippov systems (dynamical systems governed by discontinuous but piecewise smooth vector fields) stable periodic motion with sliding is not robust with respect to stable singular perturbations.…

A countable group $G$ has the strong topological Rokhlin property (STRP) if it admits a continuous action on the Cantor space with a comeager conjugacy class. We show that having the STRP is a symbolic dynamical property. We prove that a…

Geometrical properties of two-dimensional mixtures near the jamming transition point are numerically investigated using harmonic particles under mechanical training. The configurations generated by the quasi-static compression and…