54 citations · 777 across the 87 of their papers we have counts for
88 papers
On the Darboux-Halphen system: Jacobi vs Lie
A. V. Tsiganov
Two constructions of the Darboux-Halphen system are discussed. In the Jacobi construction we start with transcendental functions which are fixed as the first integrals. In the Lie…
On integrable by Euler planar differential systems
A. V. Tsiganov
The subject of our discussion is the theory of differential equations as set out in two classical Euler's textbooks "Institutiones Calculi Differentialis" and "Institutiones Calcul…
On the Lie noncommutative integrability
A. V. Tsiganov
The Lie theory of non-commutative integrability is used to reconstruct some integrable systems of ordinary differential equations in three dimensional Eucledian space. The Darboux-…
Comment on: "Stäckel and Eisenhart lifts, Haantjes geometry and Gravitation"
A. V. Tsiganov
One of the oldest methods for constructing integrable Hamiltonian systems, proposed by Jacobi, recently is being presented as a novel Stäckel lift construction related with Haantje…
Homogeneous potentials, Lagrange's identity and Poisson geometry
A. V. Tsiganov
The Lagrange identity expresses the second derivative of the moment of inertia of a system of material points through kinetic energy and homogeneous potential energy, from which fo…
Novikov equations for commuting differential operators of orders 3,4,5
G. B. Shabat, V. V. Sokolov, A. V. Tsiganov
We consider Novikov equations for commutative ring generated by differential operators of orders 3,4,5. We present an explicit Hamiltonian form of these equations. Using the method…