Braids in classical dynamics

1993/06/14 by Cristopher Moore · 291 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Braid #Braid group #Braid theory #Combinatorics #Computer science #Geometry #Mathematics #Physics #Point (geometry) #Protein Structure and Dynamics #Pure mathematics #Quantum chaos and dynamical systems #Space (punctuation) #Symmetry (geometry) #Topology (electrical circuits)

paper · doi:10.1103/physrevlett.70.3675

published in Physical Review Letters 70(24), 3675-3679 (American Physical Society)

openalex publication_date 1993/06/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/08

Abstract

Point masses moving in 2+1 dimensions draw out braids in space-time. If they move under the influence of some pairwise potential, what braid types are possible? By starting with fictional paths of the desired topology and ``relaxing'' them by minimizing the action, we explore the braid types of potentials of the form V\ensuremath∝r^\mathrm\ensuremathα from \ensuremathα\ensuremath≤-2, where all braid types occur, to \ensuremathα=2, where the system is integrable. We also discuss issues of symmetry and stability. We propose this kind of topological classification as a tool for extending the ``symbolic dynamics'' approach to many-body dynamics.

Citations

• Knotted periodic orbits in dynamical systems—I: Lorenz's equation

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