Background

The aim of ergodic theory is to understand the stochastic behavior of deterministic dynamical systems by studying the ergodic invariant probability measures of the system. For the study of ergodic theory on symbolic dynamical systems, we intend to introduce some recently developed topics in dynamical systems. In the case of audience who does not acquire the background needed, we start with considering some topological behavior and complexity of one-dimensional dynamical systems. Beginning at the conjugacy and graph representation of systems, an important invariant known as the topological entropy is introduced. Followed by the decidability of conjugacy between two systems, an application of the topological entropy, the existence of embedding or factor map between given systems, is introduced.