Hamiltonian monodromy and Morse theory
Mathematical Physics
2020-04-29 v2 math.MP
Abstract
We show that Hamiltonian monodromy of an integrable two degrees of freedom system with a global circle action can be computed by applying Morse theory to the Hamiltonian of the system. Our proof is based on Takens's index theorem, which specifies how the energy-h Chern number changes when h passes a non-degenerate critical value, and a choice of admissible cycles in Fomenko-Zieschang theory. Connections of our result to some of the existing approaches to monodromy are discussed.
Cite
@article{arxiv.1901.00705,
title = {Hamiltonian monodromy and Morse theory},
author = {Nikolay Martynchuk and Henk W. Broer and Konstantinos Efstathiou},
journal= {arXiv preprint arXiv:1901.00705},
year = {2020}
}