Article · Zenodo · August 31, 2026

Topological Stability And The Structural Fractality of Chaos in the Two-Dimensional Three-Body Problem With Equal Masses

Mustafa Iman, Marat Zaidyn, Nurzhan Ussipov

Abstract

The article explores the underlying structure of chaos in the planar three-body problem with equal masses. Challenging the traditional view of chaotic domains as unstructured voids, the authors apply high-resolution Finite-Time Lyapunov Exponent (FTLE) mapping to reveal that chaotic phase space is strictly governed by a rigid, topological skeleton of invariant manifolds. The study identifies a phenomenon called "structural breathing," where dynamical stability temporarily recovers near periodic orbital resonances. Furthermore, the authors validate the "Skeleton Attractor Hypothesis" by demonstrating cross-scale self-similarity and universal symmetries across various choreographic orbit families. This research ultimately proposes a mathematical framework for shifting Artificial Intelligence models of dynamical systems away from fragile trajectory tracking toward robust phase-space manifold learning. Email of first author: mustaphaiman@mail.ru

Mathematical Dynamics and FractalsQuantum chaos and dynamical systemsChaos control and synchronizationplanar three-body problemequal masseschaos

Topological Stability And The Structural Fractality of Chaos in the Two-Dimensional Three-Body Problem With Equal Masses

Abstract

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