Some applications of universal holomorphic motions
Let \(E\) be a closed subset of the extended complex plane \(\hat\mathbb C\). Then there is a contractible complex Banach manifold, known as the Teichmüller space \(T(E)\), which was first studied by [\textit{G. Lieb}, Ph. D. dissertation, Cornell University, (1990)]. The second author, of the paper under review, \textit{S. Mitra} [J. Anal. Math. 81, 1--33 (2000; Zbl 0966.32009)] proved that \(T(E)\) can be considered as the universal parameter space for holomorphic motions of the closed set \(E\) over a simply connected complex Banach manifold. This universal property has found several applications to the study of holomorphic motions. In this paper, the authors give some new applications of this universal property to the study of holomorphic motions and holomorphic dynamical systems.
scientific article