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Braids in classical dynamics. (English) Zbl 1050.37522
Summary: Point masses moving in $2+1$ dimensions trace 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 $V\propto r\sp \alpha$ from $\alpha\leq -2$, where all braid types occur, to $\alpha=2$, 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.

37N20Dynamical systems in other branches of physics
37B10Symbolic dynamics
70F10$n$-body problems
70H99Hamiltonian and Lagrangian mechanics
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