Studies on complex dynamics of transcendental entire functions and singular values

研究结果总结如下：1.Morosawa和Taniguchi考虑具有两个奇异值的结构有限超越整函数的动力学问题。特别地，他们考虑具有两个渐近值的结构有限的超越整函数，这就是所谓的复误差函数。他们研究实系数复误差函数模空间的双曲分量。进一步，Morosawa证明了某些复误差函数的Fatou分量在其边界上有一条公共曲线。2.在多项式动力学中，既不存在Baker域，也不存在游荡域。相反，在先验的整体功能中，可能存在那些。另一方面，在局部一致收敛的意义下，任何超越整函数都可以用多项式序列逼近。Morosawa考虑这样的序列…的Fatou集的Caratheodory收敛和Julia集的Hausdorff收敛将多项式的S推广到某个具有Baker域和游荡域的超越整函数。3.谷口考虑结构有限的超越整函数，并研究了它们的覆盖结构和拓扑结构。他定义了一种新的一般整函数的变形空间，并讨论了结构有限整函数的变形空间的完备性和稳定性。5.Tohge考虑了多项式或有理函数的唯一值域集。他还考虑了相关结果，包括(I)分担三个值的有理函数，以及(Ii)对于不同类型的亚纯函数几乎(除例外情况外)唯一值集的集合。7.Kisaka构造了结构有限的超越整函数的射线尾。通过使用这些射线，他研究了结构有限的超越整函数的拓扑结构。8.Kisaka通过准共形运算构造了多个连通的游荡域。较少

The summary of research results is as follows.1.Morosawa and taniguchi consider dynamics of structurally finite transcendental entire functions with two singular values. In particular, they consider structurally finite transcendental entire functions with two asymptotic values, which are so-called complex error functions. They investigate hyperbolic components of the moduli space of complex error functions with real coefficients. Furthermore Morosawa proves Fatou components of certain complex error functions have a common curve in their boundaries.2.In dynamics of polynomials, there never exist Baker domains nor wandering domains. To the contrary, in that of transcendental entire functions, there may exists those. On the other hand, any transcendental entire function can be approximated by some sequences of polynomials in the sense of locally uniformly convergence. Morosawa considers the Caratheodory convergence of Fatou sets and the Hausdorff convergence of Julia sets of such sequence … More s of polynomials to a certain transcendental entire function which have a Baker domain and wandering domains.3.Taniguchi considers structurally finite transcendental entire functions and investigates their covering structure and topological structure. He defines a new kind of the deformation space of a general entire function, and discuss about completeness and stability of such deformation spaces in case of structurally finite entire functions.5.Tohge considers unique range sets for polynomials or rational functions. He also considers related results, including (i) rational functions that share three values, and (ii) sets which are almost(apart from exceptional cases) unique range seta for different classes of meromorphic functions.7.Kisaka constructs ray tails for structurally finite transcendental entire functions. By using these rays, he investigates topological structures for structurally finite transcendental entire functions.8.Kisaka constructs multiply connected wandering domains by using quasi-conformal surgeries. Less