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arXiv · 1901.00705

Hamiltonian monodromy and Morse theory

Nikolay Martynchuk·Henk W. Broer·Konstantinos Efstathiou
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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.

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Nikolay Martynchuk, Henk W. Broer, Konstantinos Efstathiou. 2019-01-03. Hamiltonian monodromy and Morse theory. https://doi.org/10.1007/s00220-019-03578-2

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