69 citations · 222 across the 18 of their papers we have counts for
22 papers
The Weighted Walks in Quadrant with Finite Groups: an Algebro-Geometric Approach
Vladimir Dragovic, Milena Radnovic
We classify weighted small-step lattice walks in the quadrant whose associated birational group is finite. Using an algebro-geometric description of the kernel curves and Cayley-ty…
Poncelet porism in singular cases
Vladimir Dragovic, Milena Radnovic
The celebrated Poncelet porism is usually studied for a pair of smooth conics that are in a general position. Here we discuss Poncelet porism in the real plane - affine or projecti…
Billiard Ordered Games and Books
Vladimir Dragovic, Sean Gasiorek, Milena Radnovic
The aim of this work is to put together two novel concepts from the theory of integrable billiards: billiard ordered games and confocal billiard books. Billiard books appeared rece…
Resonance of ellipsoidal billiard trajectories and extremal rational functions
Vladimir Dragovic, Milena Radnovic
We study resonant billiard trajectories within quadrics in the -dimensional Euclidean space. We relate them to the theory of approximation, in particular the extremal rational f…
Integrable Billiards on a Minkowski Hyperboloid: Extremal Polynomials and Topology
Vladimir Dragovic, Sean Gasiorek, Milena Radnovic
We consider billiard systems within compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We derive conditions for elliptic periodicity f…
From formal to actual Puiseux series solutions of algebraic differential equations of first order
Vladimir Dragovic, Renat Gontsov, Irina Goryuchkina
The existence, uniqueness and convergence of formal Puiseux series solutions of non-autonomous algebraic differential equations of first order at a nonsingular point of the equatio…