Hamiltonian dynamics generated by Vassiliev invariants
type: Item
instance of: scholarly article
title: Hamiltonian dynamics generated by Vassiliev invariants
zbMATH Open document ID: 0984.70016
DOI: 10.1088/0305-4470/34/7/310
author: Mitchell A. Berger
published in: Journal of Physics A: Mathematical and General
publication date: 2001-06-06T00:00:00Z
Mathematics Subject Classification ID: 70H99
Mathematics Subject Classification ID: 57M27
zbMATH DE Number: 1602302
zbMATH Keywords: knot invariants
zbMATH Keywords: Vassiliev invariants
zbMATH Keywords: topological invariants
zbMATH Keywords: Hamiltonian dynamics
zbMATH Keywords: braiding motion of three particles
zbMATH Keywords: higher-order winding numbers
zbMATH Keywords: Vassiliev-Kontsevich integrals
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1088/0305-4470/34/7/310
OpenAlex ID: W2058405949
review text: The author uses complex-valued approach to Hamiltonian dynamics in order to study the braiding motion of three particles, in connection with higher-order winding numbers. These winding numbers are related to various invariants known in topology and knot theory, for example Massey and Milnor numbers, and can be derived from Vassiliev-Kontsevich integrals [\textit{M. Kontsevich}, Gelfand, Sergej (ed.) et al., I. M. Gelfand seminar. Part 2: Papers of the Gelfand seminar in functional analysis held at Moscow University, Russia, September 1993. Providence, RI: American Mathematical Society. Adv. Sov. Math. 16(2), 137-150 (1993; Zbl 0839.57006)]. The paper contains five very interesting diagrams, but some figures are available in colour only in the electronic version of this paper at www.iop.org.
reviewed by: Mircea Crasmareanu
description: scientific article; zbMATH DE number 1602302