This note concerns uniform equicontinuity of families of operators on a separable Hilbert space H , and of families of maps on B(H). It is shown that the a one parameter group is uniformly equicontinuous if and only if the group of unitaries which implements it is so. A “geometrical” necessary and sufficient condition is given for a family of operators to be uniformly equicontinuous.

This note concerns uniform equicontinuity of families of operators on a separable Hilbert space H , and of families of maps on B(H). It is shown that a one parameter group of automorphisms is uniformly equicontinuous if and only if the group of unitaries which implements it is so. A “geometrical” necessary and sufficient condition is given for a family of operators to be uniformly equicontinuous.

This paper studies directional dynamics on one-dimensional cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule (temporal action) and the shift map (spacial action): qualitative behaviours inherited from topological dynamics (equicontinuity, sensitivit...

Riemannian foliations occupy an important place in geometry. An excellent survey is A. Haefliger’s Bourbaki seminar [11], and the book of P. Molino [18] is the standard reference for Riemannian foliations. In one of the appendices to this book, E. Ghys proposes the problem of developing a theory of equicontinuous foliated spaces paralleling that of Riemannian foliations; he uses the suggestive ...

Let f be a continuous map of the circle to itsel Necessary and sufficient conditions are given for the family ofiterates {f"}= to be equicontinuous.