Geodesic
The Rotation Number Integer Quantization Effect in Braid Groups
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 197-210

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V. M. Buchstaber, O. V. Karpov, and S. I. Tertychnyi initiated the study of the rotation number integer quantization effect for a class of dynamical systems on a torus that includes dynamical systems modeling the dynamics of the Josephson junction. Focusing on this effect, we initiate the study of a similar rotation number quantization effect for a class of groups acting on the circle, including Artin's braid groups. 
@article{TM_2019_305_a9,
     author = {A. V. Malyutin},
     title = {The {Rotation} {Number} {Integer} {Quantization} {Effect} in {Braid} {Groups}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {197--210},
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     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2019_305_a9/}
}
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A. V. Malyutin. The Rotation Number Integer Quantization Effect in Braid Groups. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 197-210. http://geodesic.mathdoc.fr/item/TM_2019_305_a9/