Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Agafonov Sergey"'
We show that if $n$ functionally independent commutative quadratic in momenta integrals for the geodesic flow of a Riemannian or pseudo-Riemannian metric on an $n$-dimensional manifold are simultaneously diagonalisable at the tangent space to every p
Externí odkaz:
http://arxiv.org/abs/2403.14319
Autor:
Agafonov, Sergey I.
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 leaves are common zero directions of the integrals. We prove that, under s
Externí odkaz:
http://arxiv.org/abs/2403.01459
Publikováno v:
E3S Web of Conferences, Vol 273, p 04008 (2021)
An analysis of the situation in one of the regions of the Russian Federation was carried out on the basis of the official information available. Mortality in the region has been declining for several years until 2020. However, the trend continued in
Externí odkaz:
https://doaj.org/article/b31ea7411346446ea3f6f28b1c4892ca
Publikováno v:
E3S Web of Conferences, Vol 273, p 09034 (2021)
The active spread of digital technologies all over the world, the mobile availability of high-speed Internet have caused a sharp increase in the time the population spends at the screens of smartphones, tablets, televisions and other media devices. I
Externí odkaz:
https://doaj.org/article/81468b5e14dc44d0b4dbbfe28ea258eb
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 corresponding to constant gaussian curvature. We give also a geometric
Externí odkaz:
http://arxiv.org/abs/2306.17540
Autor:
Agafonov, Sergey I.
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 circular 3-webs. The main results is the classification of hexagonal circula
Externí odkaz:
http://arxiv.org/abs/2306.11707
Autor:
Agafonov, Sergey I.
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 commuting flows are Darboux integrable if and only if the Laplace transf
Externí odkaz:
http://arxiv.org/abs/2105.14496
Autor:
Agafonov, Sergey I.
We present a geometric interpretation of integrability of geodesic flow by quadratic integrals in terms of the web theory and construct integrable billiards on surfaces admitting such integrals.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2004.12374
Autor:
Agafonov, Sergey I.
Publikováno v:
In Differential Geometry and its Applications December 2023 91
Autor:
Agafonov, Sergey I.
Confocal conics form an orthogonal net. Supplementing this net with one of the following: 1) the net of Cartesian coordinate lines aligned along the principal axes of conics, 2) the net of Apollonian pencils of circles whose foci coincide with the fo
Externí odkaz:
http://arxiv.org/abs/1912.01817