Continued \(g\)-fractions and geometry of bounded analytic maps

DOI10.1007/S10883-013-9200-9zbMath1326.37014arXiv1210.4805OpenAlexW2139432729MaRDI QIDQ457170

Alexei Tsygvintsev

Publication date: 26 September 2014

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

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. As an application, the Sundman-Poincar'e method in the Newtonian three-body problem is revisited and applications to collision detection problem are considered.

Full work available at URL: https://arxiv.org/abs/1210.4805

zbMATH Keywords

three-body problemcontinued fractionsreal analytic functions

Mathematics Subject Classification ID

Three-body problems (70F07) Continued fractions and generalizations (11J70) Moment problems and interpolation problems in the complex plane (30E05) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Collisions in celestial mechanics, regularization (70F16)

Cites Work

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• On the convergence of continued fractions at Runckel's points
• Continued fractions and solutions of the Feigenbaum-Cvitanović equation
• Bounds on the unstable eigenvalue for the asymmetric renormalization operator for period doubling

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