Hamiltonian Monodromy and Morse Theory - Martynchuk, Nikolay; Broer, H. W.; Efstathiou, K. (Communications in Mathematical Physics, 2019)
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.
CRIS-Team WoS Importer:2019-10-18