7 citations · 19 across the 16 of their papers we have counts for
25 papers
On complex algebraic caustics in planar and projective billiards
Alexey Glutsyuk
A caustic of a billiard is a curve whose tangent lines are reflected to its own tangent lines. A billiard is called Birkhoff caustic-integrable, if there exists a topological annul…
On germs of constriction curves in model of overdamped Josephson junction, dynamical isomonodromic foliation and Painlevé 3 equation
Alexey Glutsyuk
B.Josephson (Nobel Prize, 1973) predicted tunnelling effect for a system (called Josephson junction) of two superconductors separated by a narrow dielectric: existence of a supercu…
On rationally integrable planar dual multibilliards and piecewise smooth projective billiards
Alexey Glutsyuk
The billiard flow in a planar domain acts on its tangent bundle as geodesic flow with reflections from the boundary. Its trivial first integral is the squared velocity. Bolotin's C…
On rationally integrable planar dual and projective billiards
Alexey Glutsyuk
A caustic of a strictly convex planar bounded billiard is a smooth curve whose tangent lines are reflected from the billiard boundary to its tangent lines. The famous Birkhoff Conj…
Open problems on billiards and geometric optics
M. Bialy, C. Fierobe, A. Glutsyuk +3
This is a collection of open problems from workshop "Differential Geometry, Billiards, and Geometric Optics" at CIRM on October 4-8, 2021.
On infinitely many foliations by caustics in strictly convex open billiards
Alexey Glutsyuk
Reflection in strictly convex bounded planar billiard acts on the space of oriented lines and preserves a standard area form. A caustic is a curve whose tangent lines are refle…