arXiv subjects

Vsevolod V. Shevchishin

Publications and source records attributed to Vsevolod V. Shevchishin.

3 recordsLinked to original sources

arXiv2010

Two-dimensional superintegrable metrics with one linear and one cubic integral

We describe all local Riemannian metrics on surfaces whose geodesic flows are superintegrable with one integral linear in momenta and one integral cubic in momenta. We also show that some of these metrics can be extended to the 2-sphere. This gives us new examples of Hamiltonian systems on the sphere with integrals of degree three in momenta, and the first examples of superintegrable metrics of nonconstant curvature on a closed surface

math-ph↗

arXiv2009

Differential invariants for cubic integrals of geodesic flows on surfaces

We construct differential invariants that vanish if and only if the geodesic flow of a 2-dimensional metric admits an integral of 3rd degree in momenta with a given Birkhoff-Kolokoltsov 3-codifferential.

math.DG↗

arXiv2004

Regular homotopy of Hurwitz curves

We prove that any two irreducible cuspidal Hurwitz curves $C_0$ and $C_1$ (or more generally, curves with A-type singularities) in the Hirzebruch surface $F_N$ with coinciding homology classes and sets of singularities are regular homotopic; and symplectically regular homotopic if $C_0$ and $C_1$ are symplectic with respect to a compatible symplectic form.

math.SG↗