Studies on complex dynamics of transcendental entire functions

从有理函数动力学与超越整函数动力学的区别出发，主要研究了超越整函数的复动力学。奇异值在研究复杂动力学中起着重要作用。它们是临界值或渐近值，后者只出现在超越整函数的情况下。研究了具有两个奇异值的整函数族，得到了参数空间中双曲分量的一些结果。此外，如果超越整函数有Siegel圆，则证明了无界Siegel圆与渐近值之间的关系。

From the view point of the difference between dynamics of rational functions and those of transcendental entire functions, I mainly studied complex dynamics of transcendental entire functions. Singular values play important roles in studying complex dynamics. They are critical values or asymptotic values and the latter appear in the only case of transcendental entire functions. I investigated families of entire functions with two singular values and obtained some results on hyperbolic components of the parameter spaces. Furthermore, I showed a relationship between unbounded Siegel disks and asymptotic values, if transcendental entire functions have Siegel disks.