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The analytic structure of dynamical systems and self-similar natural boundaries. (English) Zbl 0538.58031
Summary: In this paper we investigate the analytic, complex-time structure of the movable singularities for several dynamical systems. In general, it is found that there exists a direct connection between the occurrence of a certain type of multiple-valuedness of the singularities and the existence of a class of remarkable, ”self-similar” natural boundaries for these systems. An asymptotic description of the distribution of singularities in the natural boundary is developed. This provides a description of the fine-scale structure of these natural boundaries that agrees closely with the numerical calculations.

MSC:
37-XX Dynamical systems and ergodic theory
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