In recent years there is a considerable interest on the dynamics over non-Archimedean fields. Topologically the algebraically closed and complete are always totally disconnected and not locally compact. In 1990 Berkovich introduced a new space, which is compact, path-connected and contains the non-Archimedean fields as dense subspaces in the sense of Gel'fand topology. The study of the dynamical systems over Berkovich space is a completely new topic. In this paper we shall survey the theory of iteration of non-Archimedean transcendental entire maps, and discuss recent progress and some unsolved problems.
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