Some Dimensional Properties Of Moran Fractals

In this dissertation, we mainly study some dimensional properties on Moran fractal sets. It is about the quasisymmetric property of some nonhomogeneous Moran subset whose Hausdorff dimension is 1 and the full dimensional property on some accumulation points.In Chapter 1, we briefly review the fractal naissance and give some fundamental concepts, properties of the fractal dimension and the latest conclusions, the measure theory and some difference between them.In Chapter 2, we introduce some concepts and relative properties on Moran sets, some research results of the authors all the world.In Chapter 3, in the basis of uniform Cantor sets, by suppose a condition, we proved that some non-homogeneous Moran sets are also quasisymmetric. At the end of the paper, we give an example in order to illustrate our's demonstrate which satisfies the condition.In Chapter 4, we consider the Hausdorff dimension property of a class of fractals associated with some accumulation points. By constructing some homogenenous Moran subset, we prove that these fractals have full dimension.