Uniform measures are defined as the functionals on the space of bounded uniformly continuous functions that are continuous on bounded uniformly equicontinuous sets. If every cardinal has measure zero then every countably additive measure is a uniform measure. The functionals sequentially continuous on bounded uniformly equicontinuous sets are exactly uniform measures on the separable modificati...

We characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with finite local complexity the only equicontinuous systems are then shown to be the crystalline ones. On the other hand, within the class without finite local complexity, we exhibit examples of equicontinuous minimal Delone dynamical s...

‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...

Abstract We consider the derivative nonlinear Schrödinger equation in one spatial dimension, which is known to be completely integrable. prove that orbits of $L^2$ bounded and equicontinuous sets initial data remain equicontinuous, not only under this flow, but also entire hierarchy. This allows us remove small-data restriction from prior conservation laws global well-posedness results.

We define recurrence for a compactly generated para-topological group G acting continuously on locally compact Hausdorff space X with dimX=0, and then we show that if Gx‾ is all x∈X, the conditions are pairwise equivalent: (i) this dynamic pointwise recurrent, (ii) union of G-minimal sets, (iii) G-orbit closure relation closed in X×X, (iv) X∋x↦Gx‾∈2X continuous. Consequently, product it regular...

There has always been a lack of examples of compact manifolds which are minimal sets under the action of the real line, minimal meaning that each orbit is dense in the manifold. All tori admit such an action and G. A. Hedlund [4] has given examples of 3-manifolds having such an action. The action of a group T on a metric space X is said to be distal if for any two distinct points x, y&X the dis...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...