10 citations · 51 across the 31 of their papers we have counts for
5 papers · 1 filter
Classes of integrable metrics on Banach spaces
A. Konyaev, P. Topalov
We introduce a large new class of (weak) metrics on the Hardy space that have infinite families of conservation laws in involution. The construction of the metrics and the integral…
Integrable metrics with potentials on the Hardy space and a class of PDEs
A. Konyaev, P. Topalov
We introduce a new class of quadratic in the momenta Hamiltonians with potential on Banach spaces of infinite dimension which possess an infinite family of conserved quantities in…
Elliptic non-degeneracy and spectral rigidity of classical billiards
Georgi Popov, Peter Topalov
In this paper we show that the billiard ball map of the Liouville billiard tables of classical type on the ellipsoid is non-degenerate at the elliptic fixed point. As a corollary w…
On the Integral Geometry of Liouville Billiard Tables
G. Popov, P. Topalov
The notion of a Radon transform is introduced for completely integrable billiard tables. In the case of Liouville billiard tables of dimension 3 we prove that the Radon transform i…
Analyticity of Riemannian exponential maps on ${\rm Diff}(\T)$
T. Kappeler, E. Loubet, P. Topalov
We study the exponential maps induced by Sobolev type right-invariant (weak) Riemannian metrics of order on the Lie group of smooth, orientation preserving diffeomorphisms…