Dynamics of McMullen maps

In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive answer to a question of Devaney. Higher regularity of this boundary is obtained in almost all cases. We show that the boundary is a quasi-circle if it contains neither a parabolic point nor a recurrent critical point. For the whole Julia set, we show that the McMullen maps have locally connected Julia sets except in some special cases.Comment: Complex dynamics, 51 pages, 13 figure

Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps

We give three families of parabolic rational maps and show that every Cantor set of circles as the Julia set of a non-hyperbolic rational map must be quasisymmetrically equivalent to the Julia set of one map in these families for suitable parameters. Combining a result obtained before, we give a complete classification of the Cantor circles Julia sets in the sense of quasisymmetric equivalence. Moreover, we study the regularity of the components of the Cantor circles Julia sets and establish a sufficient and necessary condition when a component of a Cantor circles Julia set is a quasicircle.Comment: 39 pages, 10 figures and 1 table, to appear in Discrete and Continous Dynamical Systems-

Twice Dynamic Consolidation — An Unusual Application in Treating Liquefiable Saturated Sandy Loam Deposits

More innovative methods of ground treatment have replaced traditional methods. Dynamic consolidation, for example, has been applied widespreadly in China. Presented in this paper is a case history of adopting the twice dynamic consolidation method to improve liquefiable saturated loesslike sandy loam deposit, since the site for the Aluminum Material Company which is located at the suburb of Talyuan, China, Is geotechnically adverse. In this project the effective depth of improvement increased significantly. Judged from the ln-situ investigation and laboratory triaxial shear test, the liquefaction potential was eliminated as predicted