10 citations · 33 across the 18 of their papers we have counts for
21 papers
Hexagonal 3-webs of circles with polar twisted cubic
Sergey I. Agafonov
The paper describes and classifies hexagonal circular 3-webs on unit sphere such that the polar points of the web circles lie on a twisted cubic, thus completing classification of…
Integrable geodesic flows with simultaneously diagonalisable quadratic integrals
Sergey I. Agafonov, Vladimir S. Matveev
We show that if functionally independent commutative quadratic in momenta integrals for the geodesic flow of a Riemannian or pseudo-Riemannian metric on an -dimensional mani…
Integrable geodesic flow in 3D and webs of maximal rank
Sergey I. Agafonov
We characterize geodesic flows, admitting two commuting quadratic integrals with common principal directions, in terms of the geodesic 4-webs such that the tangents to the web leav…
Fractional-linear integrals of geodesic flows on surfaces and Nakai's geodesic 4-webs
Sergey I. Agafonov, Thaís G. P. Alves
We prove that if the geodesic flow on a surface has an integral, fractional-linear in momenta, then the dimension of the space of such integrals is either 3 or 5, the latter case c…
Hexagonal Circular 3-Webs with Reducible Polar Curves of Degree Three
Sergey I. Agafonov
The paper reports the progress with the classical problem, posed by Blaschke and Bol in 1938. We present new examples and new classifications of natural classes of hexagonal circul…
Darboux integrability for diagonal systems of hydrodynamic type
Sergey I. Agafonov
We prove that 1) diagonal systems of hydrodynamic type are Darboux integrable if and only if the corresponding systems for commuting flows are Darboux integrable, 2) systems for co…