Complete Semi-Dynamical Systems

Abstract

In this paper generalized vector fields are studied. The notion of left invariant vector fields is extended by the use of top spaces. As a result a new kind of dynamics is extrapolated. By the topological properties of topological generalized groups, topological complete semi-dynamical'systems are studied. A method for constructing a complete semi-dynamical system on a generalized coset space is deduced. An application in the genetic space and the whether system are considered.

Asymptotic Dynamics Via a Time Set Without any Order

“…Let s ∈ G be given. Since lim n→∞ ϕ s n (x) = l and ϕ s is a continuous map, The assumptions of theorem 1 and theorem 2 can appear in the class of topological complete semi-dynamical systems [6]. Let us to recall the definition of complete semi-dynamical system.…”

“…If S is a completely simple semigroup, and (X, D = {ϕ s : s ∈ S}) is a semidynamical system, then (X, D) is called a complete semi-dynamical system [6] if for given x ∈ X there exists s ∈ S such that ϕ s (x) = x.…”

Some Algebraic Properties of Generalized Rings

“…The properties (i), (ii), and (iii) mean that (R, +) is a generalized group or completely simple semigroup (see [4,5]). This notion has been applied in geometry (see [8,9]) and dynamical systems (see [6]).…”

On the quotient space of a generalized action of a generalized group

“…The role of identity as a mapping made many new important challenges. Generalized groups have been applied in genetic [1,12], geometry [11] and dynamical systems [13]. The notion of generalized action [8] is an extension of the notion of group actions [3,6].…”