Study on dynamical behavior of Sturmian System

摘要

Symbolic dynamics is an iterative system that is generated by a shift on a finite symbolic space. It is a special kind of dynamics. Symbolic dynamics has a lot of theoretical and practical applications in many fields such as physics, computer and so on, so it is important to study its dynamical behavior. Sturmian System is the least complex kind of symbolic dynamics. In the present paper it proves that Sturmian System is a minimal system that has zero entropy and is not chaotic. According to some concepts on Symbolic Dynamics and properties of minimal nonchaotic on Sturmian System, we make a kind of subshift that generated by a nonperiodic recurrent orbit and study its properties. If a period point exists a subshift generated by a nonperiodic recurrent orbit, it is not certain that the subshift contains an uncountable scrambled set.