The topological transitivity of non-compact group extensions of topologically mixing subshifts of finite type has been studied recently by Niţică. We build on these methods, and give the first examples of stably transitive non-compact group extensions of hyperbolic dynamical systems. Our examples include extensions of hyperbolic basic sets by the Euclidean group SE(n) for n even, n ≥ 4.

We define a variant of Lamport’s Temporal Logic of Actions, extended by spatial modalities, that is intended for the specification of mobile systems with distributed state. We discuss notions of refinement appropriate for mobile systems, specifically concerning the topological structure of the system, and show how these can be represented in the logic via quantification and implication, ensurin...

In this paper the notion of minimality is extended to relative semi-dynamical systems. We consider transitivity from the point of view of an observer which is a fuzzy set. Relative topological entropy of a relative semi-dynamical system as an invariant object of relative conjugate relations is studied. Finally illustrated example in polynomial functions is given to explain the idea of the paper.

In this article, we provide a simple geometric proof of the following fact: The existence transitive normalized maps induced by linear operators is possible only when underlying space's real dimension either 1 or 2 infinity. A similar result holds for projective transformation as well.

Let X be a compact metric space, let φ be a continuous self-map on X , and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between various dynamical properties of a given (crisp) dynamical system (X,φ) and its Zadeh’s extension Φ on F(X). Among other things we study various (weak, strong, mild etc.) mixing properties and also s...

We study various mixing properties for subshifts, which allow words in the language to be concatenated into a new word in the language given certain gaps between them. All are defined in terms of an auxiliary gap function f : N → N, which gives the minimum required gap length as a function of the lengths of the words on either side. In this work we focus mostly on topological transitivity, topo...