On monodromy in integrable Hamiltonian systems

Martynchuk, N., 2018, [Groningen]: Rijksuniversiteit Groningen. 121 p.

Research output: ThesisThesis fully internal (DIV)Academic

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  • Nikolay Martynchuk
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.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Broer, Hendrik, Supervisor
  • Efstathiou, Konstantinos, Co-supervisor
  • Fomenko, A.T., Assessment committee, External person
  • Knauff, E. A. H., Assessment committee, External person
  • Vegter, Gert, Assessment committee
Award date21-Sep-2018
Place of Publication[Groningen]
Print ISBNs978-94-034-0889-7
Electronic ISBNs978-94-034-0888-0
Publication statusPublished - 2018

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