Title: Non-Birkhoff periodic orbits in symmetric planar billiards
Abstract: A classical result of Poincaré and Birkhoff implies that every smooth convex planar billiard admits at least two periodic orbits of any rational rotation number. These orbit are called Birkhoff orbits and they admit a simple geometric description: they have the shape of regular polygon. In this talk I will present results on the existence of non-Birkhoff periodic orbits in symmetric convex planar billiards. The main result is a quantitative criterion for the existence of such orbits with prescribed period, rotation number, and spatiotemporal symmetry. As a corollary we prove that arbitrarily small analytical perturbations of the circular billiard have non-Birkhoff orbits of any rational rotation number. This is joint work with Casper Oelen and Mattia Sensi.
Bio:
- Education:
2003: PhD in Mathematics, Utrecht University. Advisors: Ferdinand Verhulst and Hans Duistermaat
1999: MSc/BSc in Mathematics, Utrecht University, cum laude
Faculty and postdoctoral positions:
2016 – … : Full professor, Vrije Universiteit Amsterdam
2014 – 2016: Associate professor, Vrije Universiteit Amsterdam
2007 – 2014: Assistant professor, Vrije Universiteit Amsterdam
2004 – 2007: Postdoc, Imperial College London - Grants and prizes
SMRI International visitor grant (8 kAUD), 2023
SMRI International visitor grant (12 kAUD), 2020
SIGEST outstanding paper award, awarded by SIAM for the article Center manifolds of coupled cell networks published in the SIAM J. Mathematical Analysis
NWO Vrije competitie grant “Variational methods for quasi-periodicity” (202 k€), 2009
NWO Veni grant “Hamiltonian lattice dynamical systems” (208 k€), 2007
MSRI Membership grant “Dynamical systems” (8 kUSD), 2007
EPSRC Postdoctoral fellowship grant “Geometry and near-integrability of Hamiltonian dynamical systems” (113 kGBP), 2004