Symbolic dynamics in a binary asteroid system

TL;DR

This paper demonstrates the presence of complex chaotic dynamics, specifically a topological horseshoe, in a binary asteroid system model through numerical methods and topological analysis.

Contribution

It introduces a novel numerical approach combining correctly aligned windows with secular problem analysis to identify chaotic behavior in binary asteroid dynamics.

Findings

Existence of a topological horseshoe in the model

Chaotic dynamics confirmed through numerical methods

Application of topological techniques to celestial mechanics

Abstract

We highlight the existence of a topological horseshoe arising from a a--priori stable model of the binary asteroid dynamics. The inspection is numerical and uses correctly aligned windows, as described in a recent paper by A. Gierzkiewicz and P. Zgliczy\'nski, combined with a recent analysis of an associated secular problem.