Recent advances in the monodromy theory of integrable Hamiltonian systems
Mathematical Physics
2020-01-30 v1 math.MP
Abstract
The notion of monodromy was introduced by J. J. Duistermaat as the first obstruction to the existence of global action coordinates in integrable Hamiltonian systems. This invariant was extensively studied since then and was shown to be non-trivial in various concrete examples of finite-dimensional integrable systems. The goal of the present paper is to give a brief overview of monodromy and discuss some of its generalisations. In particular, we will discuss the monodromy around a focus-focus singularity and the notions of quantum, fractional and scattering monodromy. The exposition will be complemented with a number of examples and open problems.
Keywords
Cite
@article{arxiv.2001.10998,
title = {Recent advances in the monodromy theory of integrable Hamiltonian systems},
author = {Nikolay Martynchuk and Henk W. Broer and Konstantinos Efstathiou},
journal= {arXiv preprint arXiv:2001.10998},
year = {2020}
}