Abstract: In this talk we explore the relation between the Laplace and the length spectra
of the domain. This relation involves the wave trace - a distribution obtained from Laplace
eigenvalues. The singularities of this distribution lie within the length spectrum and arise
from periodic billiard trajectories. We will describe how one can perturb an ellipse, such
that the contributions of several orbits to the wave trace cancel out, thus making it finitely
smooth. This shows that the length spectrum can be richer then the Laplace spectrum and that
it can be hard to hear the length spectrum of the drum.
The singular support of the wave trace and the length spectrum are often non-equal near ellipses
20.10.2023 17:00 - 18:18
Organiser:
H. Bruin, R. Zweimüller
Location:
IST Austria