Abstract
In this work, we study qualitative properties of real analytic bounded maps. The main tool is approximation of real-valued functions analytic in rectangular domains of the complex plane by continued g-fractions of Wall (1948). As an application, the Sundman–Poincaré method in the Newtonian three-body problem is revisited and applications to collision detection problem are considered.
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Tsygvintsev, A. Continued g-Fractions and Geometry of Bounded Analytic Maps. J Dyn Control Syst 20, 181–196 (2014). https://doi.org/10.1007/s10883-013-9200-9
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DOI: https://doi.org/10.1007/s10883-013-9200-9