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nlin.SI2026
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…
nlin.SI2026
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…
nlin.SI2026
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-…