L-Topological Dynamical System and Its Asymptotic Properties

Abstract

With the development of the theory of fuzzy topological space, more and more research has been focused on fuzzy topological dynamical systems. In this paper the fuzzy topological dynamical system on L-topological space is defined axiomatically in terms of an order-homomorphism mapping. This definition includes as special cases crisp single and multivalued dynamical systems on crisp topological space. Some algebraic structures of the L-topological dynamical system are summarized. It is demonstrated that orbit of system is associated with the ones of the molecules which could be used to derive the orbit of system. Meanwhile asymptotic properties of the system are investigated using convergence theory on L-topological space, and its conjugate system is discussed as well.