the main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. in this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

in this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the hypercyclicity criterion. we characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional banach space .

We proposed and analyzed implementation of the single-qutrit quantum gates based on stimulated Raman adiabatic passage (STIRAP) between magnetic sublevels in atoms coupled by pulsed laser fields. This technique requires only the control of the relative phase of the driving fields but do not involve any dynamical or geometrical phases, which make it independent of the other interaction details: ...

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...

This paper denes and investigates the ergodic proper-ties of the entropy of a countable partition of a fuzzy dynamical sys-tem at different points of the state space. It ultimately introducesthe local fuzzy entropy of a fuzzy dynamical system and proves itto be an isomorphism invariant.

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.

Let $G$ be a finite simple graph whose vertices and edges are weighted by two functions. In this paper we shall define and calculate entropy of a dynamical system on weights of the graph $G$, by using the weights of vertices and edges of $G$. We examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. At the end it is shown that, for $rin [0,+infty]$, t...

introduction: in this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. epilepsy is considered as a dynamical change in nonlinear and complex brain system. the ability of the proposed measure for characterizing the normal and epileptic eeg signals when the signal is short or is...

In this paper, we introduce the notion of relative probability measure spaces by the concept of observer. The notions of relative entropy and relative conditional entropy of countable σ-algebras are defined and studied. Using the suggested concept of relative entropy we define the relative entropy of a dynamical system and we prove some of its ergodic properties. Finally it is proved that, the ...