Studies on complex dynamics of transcendental entire functions

研究结果总结如下：1。Morosawa考虑了复杂误差函数的动力学。他特别研究了实系数函数的参数空间。他得到了参数空间中沿双曲分量边界的抛物分岔的结果。复误差函数属于Taniguchi定义的结构有限全函数族。具有两个奇异值的结构有限完整函数分为三类；复杂的误差函数，简单装饰指数映射和三次多项式。Morosawa和Taniguchi研究了具有两个奇异值的结构有限整体函数参数空间中的双曲分量。他们得到了捕获型双曲分量的结果，并发表了论文。谷口考虑了有理函数的复盖结构、全函数的复盖结构和动态结构，并研究了它们之间的关系。他还给出了渐近Teichimiiller空间的一个模型。改进了平面上定义的亚纯函数唯一性定理的条件。特别地，他从角域上的条件得到了两个函数的关系的结果。Kisaka利用改进的拟共形手术构造了具有双连通游荡域的超越全函数，更一般地，构造了具有n倍连通游荡域的超越全函数。他还利用奇异值轨道给出了超越整个函数的半双曲性的刻画。石崎研究了值分布理论和复杂动力学理论中施罗德方程解的性质之间的关系。

The summary of research results is as follows.1. Morosawa considers dynamics of complex error functions. In particular, he studies the parameter space of those functions with real coefficients. He obtains results on parabolic bifurcations along boundaries of hyperbolic components in the parameter space.2. Complex error functions belong to the family of the structurally finite entire functions, which is defined by Taniguchi. Structurally finite entire functions with two singular values are classified into three types; complex error functions, simply decorated exponential maps and cubic polynomials. Morosawa and Taniguchi study the hyperbolic components in the parameter space of structurally finite entire functions with two singular values. They obtain results on hyperbolic component of capture type and prepare a paper.3. Taniguchi considers covering structure of rational functions and entire functions and those dynamical structure and studies those relationships. He also gives a model of asymptotic Teichimiiller space.4. Tohge improves the condition on the uniqueness theorem of meromorphic functions defined in the plane. In particular, he obtains a result on a relations of two functions which comes from conditions on angular domains.5. Kisaka constructs transcendental entire functions with doubly connected wandering domain and, more generally, those with n-multiply connected wandering domains by using improved quasiconformal surgery. He also gives a characterization on semihyperbolicity of transcendental entire functions by using orbits of singular values.8. Ishizaki studies a relation ship between properties on solutions of the Schroder equations in value distribution theory and in theory of complex dynamics.