Let the measure algebra of a topological group G be equipped with the topology of uniform convergence on bounded right uniformly equicontinuous sets of functions. Convolution is separately continuous on the measure algebra, and it is jointly continuous if and only if G has the SIN property. On the space LUC(G)∗ which includes the measure algebra, convolution is also jointly continuous if and on...

The weak mean equicontinuity for a countable discrete amenable group G acting continuously on compact metrizable space X is studied. It shown that equicontinuity, pointwise ergodicity and uniformity are coincided. Moreover, we prove (X, G) equicontinuous if only the product system \((X \times X,G)\) equicontinuous.

This paper is concerned with homeomorphisms of Euclidean spaces onto themselves, with bounded orbits. The following results are obtained. (1) A homeomorphism of E onto itself has both bounded orbits and an equicontinuous family of iterates iff it is a conjugate of either a rotation or a reflection; (2) An example of Bing is modified to produce a fixed point free, orientation preserving homeomor...

We consider a minimal equicontinuous action of finitely generated group $ G on Cantor set X with invariant probability measure \mu $, and the stabilizers points for such an action. give sufficient conditions under which there exists subgroup H that in whose are conjugate to has full measure. The is locally quasi-analytic non-degenerate. An if its elements have unique extensions subsets uniform ...

Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on 2D CA and aims at showing that the situation is different and more complex. The main results are the existence of non sensitive CA without equicontinuous points, the nonrecursivity of sensitivity constants and the existence of CA h...

In this paper we study combinatorial constructions which lead to one-sided invertible cellular automata with di5erent dynamical behavior: equicontinuity, existence of equicontinuous points but not equicontinuity, sensitivity and expansivity. In particular, we provide a simple characterization of the class of equicontinuous invertible one-sided cellular automata and we construct families of expa...

<p>Let X be a local dendrite, and f : → map. Denote by E(X) the set of endpoints X. We show that if is countable, then following are equivalent:</p><p>(1) equicontinuous;</p><p>(2) <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAA/CAYAAACW2FpzAAAE5ElEQVRoBe2af0zUZRzH4Y671FhMMtIRGhE4rc2to1JnKbOGLn8ABRTJmL8yXdPYUKkQRFpoiKekoiOSmZqbmhWIDih3MozgD8RIcKQ...