The shift map and the symbolic dynamics and application of topological conjugacy

The aim of this paper is to prove some chaotic properties of the symbol space 2Σ and the shift map σ and on the other hand apply the topological conjugacy property of the shift map on the logistic map. We have proved that the shift map is generically δ-chaotic on 2Σ. It is also proved that 2Σ is a Cantor set and the shift map has sensitive dependence on initial conditions in an alternative way. In two other theorems we have directly proved that the dynamical system ( 2Σ,σ) has modified weakly chaotic dependence on initial conditions as well as chaotic dependence on initial conditions. Hence by topological conjugacy the dynamical system ( µFI,), for 4>µ, has those properties.