Department of Mathematics Calendar

Back to Listing

The Department of Mathematics Calendar has moved to Webtools. Anyone may submit an event by clicking the "+" button (upper right). Note: the Sponsor field is required. Just type "n/a"

All events will be reviewed before acceptance. Please email Shelby Koehne if you have any questions about submitting an event.

Note: you may search past and future events by clicking on the magnifying glass icon on the main Calendar page.

For an archive of past events:

Symplectic and Poisson geometry seminar: On the symplectic equivalences for parabolic orbits of integrable Hamiltonian systems

Event Type
wifi event
Mar 28, 2022   12:00 pm  
Nikolay Martynchuk
Joey Palmer
Parabolic orbits are the simplest examples of degenerate singularities of integrable two degree of freedom Hamiltonian systems. Yet until recently, their symplectic (and even C^\infty smooth) classification was not known. We fill in this gap and show that the action variables corresponding to such an orbit form a complete set of symplectic invariants (up to the fiberwise symplectic equivalence). This generalises an earlier result by A.V. Bolsinov, L. Guglielmi and E.A. Kudryavtseva proving this in the analytic category. The smooth case that we present is more complicated and has useful consequences for more global symplectic classification problems. 
We shall also discuss a new classification result for parabolic orbits in the analytic category; specifically, we shall give a simple normal form for such orbits up to the right symplectic equivalence. This type of equivalence is different, but closely related to the usual fiberwise (or right-left) symplectic equivalence and interestingly enough, the normal form that we obtain is not given in terms (of the asymptotics) of the action variables.
This talk is based on a recent work with Prof. E.A. Kudryavtseva.
link for robots only