4 papers
math.DS2026
On exotic rationally integrable planar dual billiards I. Complex geometry and type of dynamics
Alexey Glutsyuk
A planar dual billiard is a planar curve equipped with a family of projective involutions of the projective lines tangent to at that fix .…
math.CV2025
Uniqueness theorem for completely non-degenerate B-groups
A. A. Glutsyuk, Yu. S. Ilyashenko
We prove that a completely non-degenerate B-group is uniquely determined by its factor: two such groups with conformally equivalent factors are Möbius conjugate. A similar propert…
math.DS2024
If a Minkowski billiard is projective, it is the standard billiard
Alexey Glutsyuk, Vladimir S. Matveev
In the recent paper arXiv:2405.13258, the first author of this note proved that if a billiard in a convex domain in is simultaneously projective and Minkowski, then…
math.DS2024
On Hamiltonian projective billiards on boundaries of products of convex bodies
Alexey Glutsyuk
Let , be two bounded strictly convex bodies (open subsets) with -smooth boundaries. We consider the product $\overline K\times\o…