Topological Dynamical System (pseudo-) Transfer The Same Set

Symbol dynamics is the important component of nonlinear science, it is a strict method of studying dynamics behavior. From principle, the researcher who study nonlinear dynamics should start from symbol dynamics.In the fast development of symbol dynamics in tens of years. Finite symbol dynamical system is always the main theme of the development of symbol dynamics, at the same time, under the efforts of numerous mathematics workers, many pretty important theoretical and realistic results have reached, make the symbol dynamics developed fast.In this paper, the former two chapters have mainly talked about finite symbol dynamics, we consider dynamics / of complete definite theory in some phase space X, it map X to X, f : X —> X. So long as X is compact manifold, it has finite open covering, using different letters to name every open set of open covering, only need to use finite character set, through dynamics, various symbol sequence were formed with using this character set. The Chapter 2 and 3 of this paper has mainly talked about such limited symbol dynamical system.Besides, other mathematics workers attach great importance to expanding the concept to make system or theorem has the as weak as possible prerequisite, so as to make these system or theorem set up in more broad scope. In this paper, base space of dynamic system is improved, requiring base space is non-compact, so as to change compact symbol dynamical system or finite dynamical system to generalized symbol dynamical system, which mainly about countable symbol dynamical system. The latter chapters of this paper mainly discussed invariant subset of noncompact space, and topological conjugacy or topological semi-conjugacy of generalized symbol dynamical system.