标题：Continuity Of The Hausdor Dimensions And Topological Pressures For Non-Conformal Repellers
内容：In this paper, we prove that the Hausdorff dimensions of C1 expanding repellers are continuous at conformal repellers in C1 topology. This is a direct corollary of our main result. Some counterexamples show that they may not be continuous at some non-conformal repellers. We conjecture that this phenomena is true for all the non-conformal repellers whose Hausdorff dimension is strictly less than its singularity dimension. Meanwhile, we survey some results on the dimensions of self-affine sets and non-conformal repellers
标题：ON THE ENTROPY OF SPACING SHIFTS
内容：Spacing shifts were introduced by Lau and Zame in 1973 to provide examples of maps that are topologically weakly mixing but not mixing. Recently, it has been shown that the shift possesses a rich variety of dynamical characteristics. However, the entropy formula for the general spacing shift is still unknown. Our result has two fold. First, we characterize whether a spacing shift is entropy minimal. Second, the entropy formulae of the additive and multiplicative spacing shifts are presented.
标题：Law of the iterated logarithm for dynamical systems
内容：We prove the law of the iterated logarithm in the setting of ergodic measure preserving transformation under a mild summability condition. We apply the result to the dynamical systems with certain decay of correlations for different observations.