Recent advances in the monodromy theory of integrable Hamiltonian systems

Martynchuk N, Broer HW, Efstathiou K (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Indagationes Mathematicae Elsevier

DOI: 10.1016/j.indag.2020.05.001

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 generalizations. 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.

Authors with CRIS profile

Nikolay Martynchuk Lehrstuhl für Mathematik (Mathematische Physik)

Involved external institutions

University of Groningen / Rijksuniversiteit Groningen NL Netherlands (NL) Duke Kunshan University (DKU) CN China (CN)

How to cite

APA:

Martynchuk, N., Broer, H.W., & Efstathiou, K. (2020). Recent advances in the monodromy theory of integrable Hamiltonian systems. Indagationes Mathematicae. https://dx.doi.org/10.1016/j.indag.2020.05.001

MLA:

Martynchuk, Nikolay, H. W. Broer, and K. Efstathiou. "Recent advances in the monodromy theory of integrable Hamiltonian systems." Indagationes Mathematicae (2020).

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