Related papers: A note on mean equicontinuity
We provide sufficient conditions for a Banach space Y to be weakly sequentially complete. These conditions are expressed in terms of the existence of directional derivatives for cone convex mappings with values in Y .
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…
For a general discrete dynamics on a Banach and Hilbert spaces we give necessary and sufficient conditions of the existence of bounded solutions under assumption that the homogeneous difference equation admits an discrete dichotomy on the…
The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…
The behavior of a class of mappings of a domain of Euclidean space is studied. It is established that the indicated class is equicontinuous both at the inner and at the boundary points of the domain if the mappings contained in it satisfy…
The article is devoted to the generalization of the second Bogolyubov's theorem to non-almost periodic dynamical systems. We prove the analog of the second Bogolyubov's theorem for recurrent or pseudo recurrent dynamical systems in Banach…
It is shown that in a topological dynamical system with positive entropy, there is a measure-theoretically "rather big" set such that a multivariant version of mean Li-Yorke chaos happens on the closure of the stable or unstable set of any…
In this paper, we use a Banach fixed point theorem to obtain suficient conditions satisfying the convergence and exponential convergence of solutions for the linear system of advanced differential equations. The considered system with…
This work describes the way that topological mixing and chaos in continua, as induced by discrete dynamical systems, can or can't be understood through topological conjugacy with symbolic dynamical systems. For example, there is no symbolic…
A behavior of open discrete mappings, which are quasiconformal in the mean, is investigated. It is proved that the classes of mappings mentioned above are equicontinuous (normal).
The weak mean equicontinuous properties for a countable discrete amenable group $G$ acting continuously on a compact metrizable space $X$ are studied. It is shown that the weak mean equicontinuity of $(X \times X,G)$ is equivalent to the…
The orbit closures of regular model sets generated from a cut-and-project scheme given by a co-compact lattice $\mathcal{L}\subset G\times H$ and compact and aperiodic window $W\subseteq H$, have the maximal equicontinuous factor (MEF)…
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is…
The article is devoted to the study of mappings with finite distortion in metric spaces. Analogues of results relating to equicontinuity and normality of families of quasiregular mappings are obtained. It is proved that the indicated…
Variational relation problems allow a general approach for variational inequalities, equilibrium problems, optimization problems, variational inclusions. In this paper we consider a system of quasi-variational relations and determine some…
We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background…
We show that in case a pushdown system is bisimulation equivalent to a finite system, there is already a bisimulation equivalent finite system whose size is elementarily bounded in the description size of the pushdown system. As a…
We introduce a fairly general concept of functional equation for $k$-tuples of functions $f_1,\dots,f_k\colon X \to Y$ between arbitrary sets. The homomorphy equations for mappings between groups and other algebraic systems, as well as…
In this paper, we prove that for a topological dynamical system with positive mean topological dimension and marker property, it has factors of arbitrary small mean topological dimension and zero relative mean topological dimension which…