Mixing properties of maps with uniform shadowing property in uniform spaces
In this note we study some properties of topological entropy for noncompact non-metrizable spaces.
math.DS↗
arXiv subjects
Seyyed Alireza Ahmadi
Publications and source records attributed to Seyyed Alireza Ahmadi.
Some Properties of Recurrent Sets for Endomorphisms of Topological Groups
This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent points and chain transitive component of the identity are topological subgroups. Furthermore, it is obtained that some dynamical properties induced by the original system on quotient spaces. These results link an algebraic property to a dynamical property.
math.GN↗
Interpolating operator Jensen-type inequalities for log-convex and superquadratic functions
Motivated by some recently established operator Jensen-type inequalities related to a usual convexity, in the present paper we derive several more accurate operator Jensen-type inequalities for certain subclasses of convex functions. More precisely, we obtain interpolating series of Jensen-type inequalities for log-convex and non-negative superquadratic functions. In particular, we obtain the corresponding refinements of the Jensen-Mercer operator inequality for such classes of functions.
math.FA↗
Topological Entropy, Entropy points and shadowing
In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map $f$ of a uniform space has topological shadowing property then the map $f$ has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having shadowing property.
math.DS↗