| We always investigate minimal sets and almost periodic points in compact dynamical systems, and we find lots of good properties.Many important common spaces such as open interval and R" are not compact space, there aren't always exist minimal sets or almost periodic points in the dynamical systems that are set upon such sorts of phase spaces, and then they don't have the properties in compact dynamical systems. So we must investigate minimal sets and almost periodic points in the dynamical systems where the phase is not compact space.In Chapterl,we mainly illustrate history of dynamical systems, the background of minimal sets and almost periodic points. The purpose and main contents of the topological dynamical system are presented.In Chapter2, as f can be extended, we give the existence of minimal sets in locally compact dynamical systems(E,f) used by the minimal sets in compact dynamical (ωE, f)and give the relation with dynamical systems (ωE, f).In Chapter 3, we investigate the existence of almost periodic points in locally dynamical systems. As every point of a minimal set is almost periodic point in compact dynamical systems, so we may investigate almost periodic points in locally compact dynamical systems. We use the same method to investigate the existence of almost periodic points as we made in chapter 2.To confirm the appropriateness and explore further advantages of the conclusion in Chapter 2 and Chapter 3, we will give some examples when f can be extended in Chapter 4. We give some examples about having only one minimal set and almost periodic point, and the examples also having more than one minimal set and almost periodic point in induced compact dynamical systemsωE,f). We also give some examples about the existence of minimal sets and almost periodic points in locally compact dynamical systems when f can't be extended. Finally we summarize the results and innovation of this thesis, and present our view of perspectives for the future study. |
