Complex analytic study of real and complex dynamical systems

利用复解析方法研究了实动力系统和复动力系统的不变量集结构和分岔现象。对于一维复杂动力系统的非理性无关不动点，定义了近抛物型重整化，构造了其函数的不变空间。这个空间对应于一次穿孔盘的Teichmueller空间重整化是相对于Teichmueller度规收缩的。

We studied the structure of invariant sets and bifurcation phenomena of real and complex dynamical systems via complex analytic methods. For irrationally indifferent fixed points of one-dimensional complex dynamical systems, we defined near-parabolic renormalization and constructed its invariant space of functions. This space was shown to correspond to the Teichmueller space of once-punctured disk and the renormalization is contracting with respect to the Teichmueller metric.