Continued g-fractions and geometry of bounded analytic maps

TL;DR

This paper explores the properties of bounded real analytic functions using continued g-fractions, with applications to celestial mechanics and collision detection in the three-body problem.

Contribution

It introduces a novel approach to approximate bounded analytic maps via continued g-fractions and applies this to classical problems in celestial mechanics.

Findings

Effective approximation of real analytic functions in rectangular domains.

Revisiting the Sundman-Poincaré method with g-fractions.

Applications to collision detection in three-body systems.

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.