2006/12/29 by Annalisa Calini, Annalisa M. Calini, Thomas A. Ivey +1
Mathematics · Physics and Astronomy · #Combinatorics #Knot (papermaking) #Mathematical analysis #Mathematics #Mechanics #Nonlinear Waves and Solitons #Physics #Protein filament #Quantum chaos and dynamical systems #Quasiperiodic function #Stochastic processes and statistical mechanics #Topology (electrical circuits) #Vortex #math.DG #nlin.SI
paper · pdf · doi:10.1007/s00332-007-9002-x
33 pages, 5 figures; submitted to Journal of Nonlinear Science
arxiv created 2006/12/29 · openalex publication_date 2007/07/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.