Zobrazeno 1 - 10
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pro vyhledávání: '"Tsiganov, A."'
Autor:
Tsiganov, A. V.
We discuss global tensor invariants of a rigid body motion in the cases of Euler, Lagrange and Kovalevskaya. These invariants are obtained by substituting tensor fields with cubic on variable components into the invariance equation and solving the re
Externí odkaz:
http://arxiv.org/abs/2410.10109
Autor:
Tsiganov, A. V.
We discuss some families of integrable and superintegrable systems in $n$-dimensional Euclidean space which are invariant to $m\geq n-2$ rotations. The integrable invariant Hamiltonian $H=\sum p_i^2+V(q)$ commutes with $n-2$ integrals of motion $M_\a
Externí odkaz:
http://arxiv.org/abs/2305.12370
Autor:
Porubov, E. O., Tsiganov, A. V.
We discuss the pairs of quadratic integrals of motion belonging to the $n$-dimensional space of independent integrals of motion in involution, that provide integrability of the corresponding Hamiltonian equations of motion by quadratures. In contrast
Externí odkaz:
http://arxiv.org/abs/2301.02774
Autor:
Tsiganov, A. V.
Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant transformati
Externí odkaz:
http://arxiv.org/abs/2211.08750
Autor:
Tsiganov, Andrey V.
Publikováno v:
SIGMA 18 (2022), 094, 19 pages
We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere with a set of geodesic flows with quartic invariants. By adding various potentials to the corresponding geodesic Hamiltonians, we can constr
Externí odkaz:
http://arxiv.org/abs/2201.09576
Autor:
Porubov, E. O., Tsiganov, A. V.
Publikováno v:
Communications in Nonlinear Science and Numerical Simulation, 2022
We obtain 21 two-dimensional natural Hamiltonian systems with sextic invariants, which are polynomial of the sixth order in momenta. Following to Bertrand, Darboux, and Drach these results of the standard brute force experiments can be applied to con
Externí odkaz:
http://arxiv.org/abs/2110.12860
Autor:
Tsiganov, A. V.
Abel's quadratures for integrable Hamiltonian systems are defined up to a group law of the corresponding Abelian variety $A$. If $A$ is isogenous to a direct product of Abelian varieties $A\cong A_1\times\cdots\times A_k$, the group law can be used t
Externí odkaz:
http://arxiv.org/abs/2104.10362
Autor:
Tsiganov, A. V.
Publikováno v:
Journal of Geometry and Physics, v. 178, 104571, 2022
We study non-invariant Killing tensors with non-zero Nijenhuis torsion in the three-dimensional Euclidean space. Generalizing the corresponding integrable systems we construct two new families of superintegrable systems in $n$-dimensional Euclidean s
Externí odkaz:
http://arxiv.org/abs/2102.10272
Autor:
Tsiganov, A. V.
Publikováno v:
Regular and Chaotic Dynamics, v.27, n.3, pp. 307-319, 2022
There are a few Lax matrices of the Clebsch system. Poles of the Baker-Akhiezer function determine the class of equivalent divisors on the corresponding spectral curves. According to the Riemann-Roch theorem, each class has a unique reduced represent
Externí odkaz:
http://arxiv.org/abs/2101.09993
Autor:
Tsiganov, A. V.
In the modern theory of the Kowalevski top there are two elliptic curves introduced by Kowalevski and by Reyman and Semenov-Tian-Shansky. The Kowalevski variables of separation and poles of the Baker-Akhiezer function define two classes of linearly e
Externí odkaz:
http://arxiv.org/abs/2009.09624