Hamiltonian Monodromy and Morse Theory

Martynchuk N, Broer HW, Efstathiou K (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

DOI: 10.1007/s00220-019-03578-2

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.

Authors with CRIS profile

Nikolay Martynchuk Lehrstuhl für Mathematik (Mathematische Physik)

Involved external institutions

University of Groningen / Rijksuniversiteit Groningen NL Netherlands (NL)

How to cite

APA:

Martynchuk, N., Broer, H.W., & Efstathiou, K. (2019). Hamiltonian Monodromy and Morse Theory. Communications in Mathematical Physics. https://dx.doi.org/10.1007/s00220-019-03578-2

MLA:

Martynchuk, Nikolay, H. W. Broer, and K. Efstathiou. "Hamiltonian Monodromy and Morse Theory." Communications in Mathematical Physics (2019).

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