Publication
Title
Symplectic classification of coupled angular momenta
Author
Abstract
The coupled angular momenta are a family of completely integrable systems that depend on three parameters and have a compact phase space. They correspond to the classical version of the coupling of two quantum angular momenta and they constitute one of the fundamental examples of so-called semitoric systems. Pelayo and Vu Ng9c have given a classification of semitoric systems in terms of five symplectic invariants. Three of these invariants have already been partially calculated in the literature for a certain parameter range, together with the linear terms of the so-called Taylor series invariant for a fixed choice of parameter values. In the present paper we complete the classification by calculating the polygon invariant, the height invariant, the twisting-index invariant, and the higher-order terms of the Taylor series invariant for the whole family of systems. We also analyse the explicit dependence of the coefficients of the Taylor series with respect to the three parameters of the system, in particular near the Hopf bifurcation where the focus-focus point becomes degenerate.
Language
English
Source (journal)
Nonlinearity. - Bristol
Publication
Bristol : Institute of Physics , 2020
ISSN
0951-7715
Volume/pages
33 :1 (2020) , p. 417-468
ISI
000632837000002
Full text (Publisher's DOI)
Full text (open access)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Project info
Modern symplectic geometry in integrable Hamiltonian dynamical systems.
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 17.10.2018
Last edited 06.09.2021
To cite this reference