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- W2894910708 abstract "In the context of integrable Hamiltonian systems, the notion of monodromy goes back to Duistermaat, who defined this invariant as the first obstruction to the existence of good global coordinates in such systems; the coordinates are known as global action-angle coordinates in the literature. Since then the notion of monodromy has received considerable interest and has also been generalized in several different directions. In this PhD thesis we give a systematic study of monodromy invariants in integrable Hamiltonian systems. We mainly study the following three different types of such invariants: Hamiltonian, fractional, and scattering monodromy. We provide new general methods which allow one to compute these invariants in many concrete examples of integrable systems and establish new connections to well-known mathematical theories, including Morse theory, Seifert manifolds, and scattering theory. The present thesis consists of 5 chapters. In Chapters 1-3 we study monodromy in compact integrable systems, for which the motion generically takes place on invariant tori. In Chapters 4 and 5 we consider the case of scattering systems, where the motion is unbounded. Throughout this thesis, applications of the obtained theoretical results to concrete examples of integrable Hamiltonian systems are discussed." @default.
- W2894910708 created "2018-10-12" @default.
- W2894910708 creator A5083060862 @default.
- W2894910708 date "2018-01-01" @default.
- W2894910708 modified "2023-09-23" @default.
- W2894910708 title "On monodromy in integrable Hamiltonian systems" @default.
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