Welcome
Here you will find material and references for the
course on Dynamical spectral determination and
rigidity. If you happen to find any mistakes, or
have any comments (there might be plenty!) and have
the energy to let me know, I'll be happy to fix
mistakes or answer your comments.
Notes
Here are the lecture notes
Notes
Tentative schedule
Monday July 3
Introduction and statement of the questions
Tuesday July 4
The main characters
Wednesday July 5
Hyperbolic billiards and their Lyapunov Spectrum
Thursday July 6
Determination of hyperbolic billiards
Friday July 7
Rigidity of Birkhoff Billiards
List of reading items
A. Uribe –
Trace Formulae
J. Chazarain -
Formule de Poisson pour les variétés riemanniennes
Amie Wilkinson –
Lectures on Otal's Theorem
J.-P. Otal –
The length spectrum of negatively curved manifolds (in French)
V. Guillemin, D. Kazhdan –
Some inverse spectral results for negatively curved 2-manifolds
T. Sunada (砂田 利一) –
Riemannian coverings and isospectral manifolds
R. Brooks -
The Sunada Method
S. Zelditch -
Inverse spectral problem for analytic domains II. ℤ₂–symmetric domains
S. Zelditch -
Spectral determination of analytic bi-axisymmetric plane domains
C. Guillarmou, T. Lefeuvre -
The marked length spectrum of Anosov manifolds
—, V. Kaloshin, Qiaoling Wei -
Dynamical spectral rigidity among ℤ₂–symmetric strictly convex domains close to a circle