Topological Chaos and Periodic Braiding of Almost-Cyclic Sets

2011/03/18 by Mark A. Stremler, Shane D. Ross, Piyush Grover +1 · 2 citations
Mathematics · Computer Science · Physics and Astronomy · #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #CHAOS (operating system) #Physics #Topology (electrical circuits) #Statistical physics #Theoretical physics #Mathematics #Combinatorics #Computer science

paper · doi:10.1103/physrevlett.106.114101

openalex publication_date 2011/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02

Abstract

In certain (2+1)-dimensional dynamical systems, the braiding of periodic orbits provides a framework for analyzing chaos in the system through application of the Thurston-Nielsen classification theorem. Periodic orbits generated by the dynamics can behave as physical obstructions that "stir" the surrounding domain and serve as the basis for this topological analysis. We provide evidence that, even in the absence of periodic orbits, almost-cyclic regions identified using a transfer operator approach can reveal an underlying structure that enables topological analysis of chaos in the domain.

Citations

• Topological fluid mechanics of stirring
• Pattern formation outside of equilibrium
• Braids of entangled particle trajectories
• Global shadowing of pseudo-Anosov homeomorphisms
• Almost-invariant sets and invariant manifolds — Connecting probabilistic and geometric descriptions of coherent structures in flows

Cited by

• Reynolds number effects on mixing due to topological chaos
• Braid group [wikipedia]

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• Braid analysis of chaos
• Almost Periodicity in Chaos
• Topological chaos: what may this mean ?
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