5 papers
Generalized Chapple--Euler Relation
Vladimir Dragović, Mohammad Hassan Murad
We provide a new proof of the necessary and sufficient condition for a triangle to be circumscribed about a central conic (ellipse or hyperbola), expressed in terms of the circumra…
Isoperiodic deformations of Toda curves and chains, the difference Korteweg - de Vries equation, and Seiberg-Witten theories
Vladimir Dragović, Vasilisa Shramchenko
We introduce the dynamics of Toda curves of order and derive differential equations governing this dynamics. We apply the obtained results to describe isoperiodic deformations…
Finite Groups of Random Walks in the Quarter Plane and Periodic -bar Links
Vladimir Dragović, Milena Radnović
We solve two long standing open problems, one from probability theory formulated by Malyshev in 1970 and another one from a crossroad of geometry and dynamics, of Darboux from 1879…
Minimal surfaces over the Pitot quadrilaterals
Vladimir Dragović, David Kalaj
We develop a fully explicit framework for constructing Scherk-type minimal graphs over the Pitot quadrilaterals (i.e. such that the two pairs of opposite sides have the same total…
A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions
Vladimir Dragović, Borislav Gajić, Božidar Jovanović
We consider motion of a material point placed in a constant homogeneous magnetic field restricted to the sphere . We provide a Lax representation of the equations of motio…