Housdorff Dimensions Of Sets Of Sequences

Nonlinear science a very important component of is a power system this subject, when we study the general power system, power system is not only a symbol strong and powerful research tools, but also a very worth studying very good research object. We often will sign elements, namely the power system is considered as a symbolic sequence of limited alphabet is a form of language to its study. In this paper, we study Hausdorff dimensions of sets of sequences on the basis of predecessors's work. The introductory chaper introduces the research background, we also review the former's work and the known results.In chapter 2, we introduce some basic knowledge of fractal geometry and some theorems, then we introduce a few conceptions and definitions, including Hausdorff measure, Hausdorff dimension, Self-similar sets, measure entropy, sets of sequences and symbolic space.In the next chapter, we study Hausdorff dimensions of sets of sequences. We study sequences recuring at different speed and compute their Hausdorff dimensions.These sets are uncountable. In chapter 3, we study two simple sets of sequences, and then we study two complicated sets of sequences.For every sets of sequences, we research it's subset whose Hausdorff dimension is 1, so we can study our sets of sequences . The Hausdorff dimensions of the sets which we study is 1, these are our results.