Diam-mean equicontinuity is a dynamical property that has been of use in the study non-periodic order. Using some type "local" skew product between shift and an odometer looking cellular automaton (CA), we will show there exists almost diam-mean equicontinuous CA not equicontinuous, (and hence locally periodic). As application Kurka's dichotomy does hold for versions sensitivity equicontinuity.

This article is about the interplay between topological dynamics and differential geometry. One could ask how many informations of the geometry are carried in the dynamic of the geodesic flow. M. Paternain proved in [6] that an expansive geodesic flow on a surface implies that there are no conjugate points. Instead of regarding notions that describe chaotic behavior (for example expansiveness) ...

1. Definitions. These definitions are essentially those given by Gottschalk and Hedlund (cf. [3]).1 Let X be a topological space, T a topological group with identity e, and ir a mapping of X X T into X with the properties: (1) ir(x, e)=x, (2) 7r(7r(rc, h), t2)=ir(x, tit2), (3) ir is continuous. The triple (X, T, ir) is called a transformation group (or dynamical system). Henceforth we shall wri...

A web has been defined [2] by R. L. Moore. A compact plane continuum W is said [l ] to be a simple plane web if there exist an upper semicontinuous collection G of mutually exclusive continua filling up W and another such collection H also filling up W such that (1) G is a dendron with respect to its elements and so is H and (2) if g and h are elements of G and H respectively, the common part o...

We study the set of strictly temporally periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but are not spatially periodic. This set turns out to be residual for equicontinuous surjective cellular automata, dense for almost equicontinuous surjective cellular automata, while it is empty for the positively expa...

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...

Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on an arbitrary topological group.