Research team
Expertise
My research lies at the intersection of dynamical systems and symplectic geometry. More concretely, I work with semitoric systems, a specific type of completely integrable Hamiltonian systems defined on 4-dimensional symplectic manifolds, where one of the conserved quantities induces a global circular action and other additional conditions. These systems can be classified using five symplectic invariants, but their computation is troublesome. I develop computational methods to calculate them with mathematical software, using properties of elliptic integrals and the theory of complex elliptic curves.
Modern symplectic geometry in integrable Hamiltonian dynamical systems.
Abstract
This research project studies aspects of interactions between integrable Hamiltonian systems and modern symplectic geometry: The symplectic classification in the sense of Pelayo & Vu Ngoc's is completed for two seminal examples of semitoric systems, namely the coupled spin oscillator and coupled angular momenta. In addition, more general families are studied and partially classified.Researcher(s)
- Promoter: Hohloch Sonja
- Fellow: Alonso Fernandez Jaume
Research team(s)
Project type(s)
- Research Project