A.V.Tsiganov, “The Drach superintegrable systems”, Journal of Physics A: Mathematical and General, 33:41 (2000), 7407-7422
I. V. Komarov, V. V. Sokolov, A. V. Tsiganov, “Poisson maps and integrable deformations of the Kowalevski top”, Journal of Physics A: Mathematical and General, 36:29 (2003), 8035-8048
A. V. Borisov, I. S. Mamaev, A. V. Tsyganov, “Negolonomnaya dinamika i puassonova geometriya”, UMN, 69:3 (2014), 87-144
A.V. Tsiganov, “The Kepler Problem: Polynomial Algebra of Nonpolynomial First Integrals”, Regul. Chaotic Dyn.,, 24:4 (2019), 353-369
A. V. Borisov, A. V. Tsyganov, “O dvizhenii negolonomnogo shara Chaplygina v magnitnom pole, zadache Grioli i effekte Barneta–Londona”, Doklady RAN. Fiz. tekhn. nauki, 491:1 (2020), 30-33
A. V. Tsiganov, “On tensor invariants for the Euler, Lagrange and Kowalewski cases of rigid body motion.”, Izv. RAN. Ser. Mat. (to appear)
2024
2.
A. V. Tsiganov, “On rotation invariant integrable systems”, Izv. Math., 88:2 (2024), 389–410
2023
3.
A. V. Tsiganov, E. O. Porubov, “On a class of quadratic conservation laws for Newton equations in Euclidean space”, Theoret. and Math. Phys., 216:2 (2023), 1209–1237
4.
Andrey V. Tsiganov, “Integrable Systems on a Sphere, an Ellipsoid and a Hyperboloid”, Regul. Chaotic Dyn., 28:6 (2023), 805–821;
2022
5.
A. V. Tsiganov, “On Killing tensors in three-dimensional Euclidean space”, Theoret. and Math. Phys., 212:1 (2022), 1019–1032
6.
Andrey V. Tsiganov, “Reduction of Divisors and the Clebsch System”, Regul. Chaotic Dyn., 27:3 (2022), 307–319;
7.
Andrey V. Tsiganov, “Equivalent Integrable Metrics on the Sphere with Quartic Invariants”, SIGMA, 18 (2022), 94 , 19 pp., arXiv: 2201.09576;
E. O. Porubov, A. V. Tsiganov, “On Two-Dimensional Hamiltonian Systems with Sixth-Order Integrals of Motion”, Communications in Nonlinear Science and Numerical Simulation, 110 (2022), 106404
A. V. Tsiganov, “On integrable systems outside Nijenhuis and Haantjes geometry”, Journal of Geometry and Physics, 178 (2022), 104571
2021
11.
A. V. Borisov, A. V. Tsiganov, E. A. Mikishanina, “On inhomogeneous nonholonomic Bilimovich system”, Commun. Nonlinear Sci. Numer. Simul., 94 (2021), 105573 , 11 pp. ;
A. V. Borisov, A. V. Tsiganov, “The Motion of a Nonholonomic Chaplygin Sphere in a Magnetic Field, the Grioli Problem, and the Barnett-London Effect”, Dokl. Phys., 65:3 (2020), 90–93
15.
A. V. Tsiganov, “On a Time-Dependent Nonholonomic Oscillator”, Russ. J. Math. Phys., 27:3 (2020), 399–409;
A. V. Tsiganov, “On the Mishchenko–Fomenko hypothesis for a generalized oscillator and Kepler system”, Chebyshevskii Sb., 21:2 (2020), 383–402
17.
A. V. Borisov, A. V. Tsiganov, “On rheonomic nonholonomic deformations of the Euler equations proposed by Bilimovich”, Theor. Appl. Mech., 47:2 (2020), 155–168;
A. V. Borisov, A. V. Tsiganov, “Influence of Bartnett–London and Einstein–de Haas effects on the motion of the nonholonomic sphere of Routh”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019), 583–598
2018
26.
A. V. Tsiganov, “Discretization of Hamiltonian systems and intersection theory”, Theoret. and Math. Phys., 197:3 (2018), 1806–1822
27.
A. V. Tsiganov, “Duffing Oscillator and Elliptic Curve Cryptography”, Nelineinaya dinam., 14:2 (2018), 235–241
28.
Andrey V. Tsiganov, “On Discretization of the Euler Top”, Regul. Chaotic Dyn., 23:6 (2018), 785–796
A. V. Tsiganov, “Two integrable systems with integrals of motion of degree four”, Theoret. and Math. Phys., 186:3 (2016), 383–394
34.
A. V. Tsiganov, “Abel's theorem and Bäcklund transformations for the Hamilton–Jacobi equations”, Proc. Steklov Inst. Math., 295 (2016), 243–273
35.
Yury A. Grigoryev, Alexey P. Sozonov, Andrey V. Tsiganov, “Integrability of Nonholonomic Heisenberg Type Systems”, SIGMA, 12 (2016), 112 , 14 pp., arXiv: 1603.03528
Yu. A. Grigor'ev, A. P. Sozonov, A. V. Tsiganov, “On an integrable system on the plane with velocity-dependent potential”, Nelin. Dinam., 12:3 (2016), 355–367
2015
37.
Andrey V. Tsiganov, “Separation of variables for some generalization of the Chaplygin system on a sphere”, Nelin. Dinam., 11:1 (2015), 179–185
38.
A. P. Sozonov, A. V. Tsiganov, “Bäcklund transformations relating different Hamilton–Jacobi equations”, Theoret. and Math. Phys., 183:3 (2015), 768–781
39.
A. V. Tsiganov, “Killing Tensors with Nonvanishing Haantjes Torsion and Integrable Systems”, Regul. Chaotic Dyn., 20:4 (2015), 463–475
A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “On the Nonlinear Poisson Bracket Arising in Nonholonomic Mechanics”, Math. Notes, 95:3 (2014), 308–315
43.
A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538
44.
Alexander V. Vershilov, Yury A. Grigoryev, Andrey V. Tsiganov, “On an integrable deformation of the Kowalevski top”, Nelin. Dinam., 10:2 (2014), 223–236
45.
Andrey V. Tsiganov, “On the Lie Integrability Theorem for the Chaplygin Ball”, Regul. Chaotic Dyn., 19:2 (2014), 185–197
A. V. Tsiganov, “On the Chaplygin Problem of the Rolling of a Ball”, Math. Notes, 94:4 (2013), 599–602
48.
A. V. Tsiganov, “Brief rewiev of main scientometric indices based on citations”, UBS, 44 (2013), 248–261
49.
Yu. A. Grigor'ev, V. A. Khudobakhshov, A. V. Tsiganov, “Separation of variables for some systems with a fourth-order integral of motion”, Theoret. and Math. Phys., 177:3 (2013), 1680–1692
50.
Andrey V. Tsiganov, “On the absolute dynamics of the Chaplygin ball”, Nelin. Dinam., 9:4 (2013), 711–719
2012
51.
Andrey V. Tsiganov, “New variables of separation for the Steklov–Lyapunov system”, SIGMA, 8 (2012), 12–14
A. V. Tsiganov, “On the bi-Hamiltonian structure of the Chaplygin and Borisov–Mamaev–Fedorov systems at a zero constant of areas. II”, Nelin. Dinam., 8:1 (2012), 43–55
53.
Andrey V. Tsiganov, “Superintegrable Stäckel systems on the plane: elliptic and parabolic coordinates”, SIGMA, 8 (2012), 31–9
A. V. Tsiganov, “On deformations of the canonical Poisson bracket for the nonholonomic Chaplygin and the Borisov–Mamaev–Fedorov systems on zero-level of the area integral. I”, Nelin. Dinam., 7:3 (2011), 577–599
61.
V. A. Khudobakhshov, A. V. Tsiganov, “Integrable systems on the sphere associated with genus three algebraic curves”, Nelin. Dinam., 7:1 (2011), 53–74
62.
A. J. MacIejewski, M. Przybylska, A. V. Tsiganov, “On algebraic construction of certain integrable and super-integrable systems”, Physica D: Nonlinear Phenomena, 240:18 (2011), 1426–1448
Yu. A. Grigoryev, A. V. Tsiganov, “Separation of variables for the generalized Henon-Heiles system and system with quartic potential”, Journal of Physics A: Mathematical and Theoretical, 44:25 (2011), 255202
A. V. Tsiganov, V. A. Khudobakhshov, “Integrable systems on the sphere associated with genus three algebraic curves”, Regular and Chaotic Dynamics, 16:3 (2011), 396–414
A. V. Tsiganov, “On bi-integrable natural hamiltonian systems on Riemannian manifolds”, Journal of Nonlinear Mathematical Physics, 18:2 (2011), 245–268
A. V. Tsiganov, “Comments on P. E. Ryabov “Explicit integration and topology of D. N. Goryachev case””, Nelin. Dinam., 7:3 (2011), 715–717
68.
A. V. Borisov, A. V. Tsiganov, Nelin. Dinam., 7:1 (2011), 177–187
2010
69.
A. V. Tsiganov, “New variables of separation for particular case of the Kowalewski top”, Nelin. Dinam., 6:3 (2010), 639–652
70.
A. V. Tsiganov, “On the generalized Chaplygin system”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 21, Zap. nauchn. sem. POMI, 374, POMI, SPb., 2010, 250–267
Yu. A. Grigor'ev, A. V. Tsiganov, “On the Abel equations and the Richelot integrals”, Nelin. Dinam., 5:4 (2009), 463–478
75.
A. V. Tsiganov, “Change of the time for the periodic Toda lattices and natural systems on the plane with higher order integrals of motion”, Regular and Chaotic Dynamics, 14:4-5 (2009), 541–549
A. V. Vershilov, A. V. Tsiganov, “On bi-Hamiltonian geometry of some integrable systems on the sphere with cubic integral of motion”, Journal of Physics A: Mathematical and Theoretical, 42:10 (2009), 105203
A. V. Tsiganov, “On the bi-Hamiltonian structure of the Goryachev system on the sphere”, Doklady Mathematics, 79:3 (2009), 430–433
79.
Yu. A. Grigoryev, V. A. Khudobakhshov, A. V. Tsiganov, “On Euler superintegrable systems”, Journal of Physics A: Mathematical and Theoretical, 42:7 (2009), 075202
N. A. Kostov, A. A. Tsiganov, “New Lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-Hamiltonian structure”, Regular and Chaotic Dynamics, 13:6 (2008), 593–601
A. V. Tsiganov, “A family of the Poisson brackets compatible with the Sklyanin bracket”, Journal of Physics A: Mathematical and Theoretical, 40:18 (2007), 4803–4816
A. V. Tsiganov, “On two different bi-Hamiltonian structures for the Toda lattice”, Journal of Physics A: Mathematical and Theoretical, 40:24 (2007), 008, 6395–6406
Yu. A. Grigoryev, A. V. Tsiganov, “Computing of the separated variables for the Hamilton–Jacobi equation”, Nelin. Dinam., 1:2 (2005), 163–179
103.
Yu. A. Grigoryev, A. V. Tsiganov, “Symbolic software for separation of variables in the Hamilton-Jacobi equation for the L-systems”, Regular and Chaotic Dynamics, 10:4 (2005), 413–422
A. V. Tsyganov, “A family of integrable systems on the sphere with a cubic additional integral of motion”, Doklady Akademii Nauk, 402:4 (2005), 457–459
A. V. Tsyganov, “On isomorphism of the Steklov-Lyapunov system with the potential motion on the sphere”, Doklady Akademii Nauk, 400:4 (2005), 463–466
106.
A. V. Tsiganov, “On a family of integrable systems on a sphere possessing a cubic integral of motion”, Doklady Mathematics, 71:3 (2005), 413–415
107.
A. V. Tsiganov, “A new integrable system on S2 with the second integral quartic in the momenta”, Journal of Physics A: Mathematical and General, 38:16 (2005), 3547–3553
I. V. Komarov, A. V. Tsiganov, “On a trajectory isomorphism of the Kowalevski gyrostat and the Clebsch problem”, Journal of Physics A: Mathematical and General, 38:13 (2005), 2917–2927
A. V. Tsiganov, “On a family of integrable systems on S2with a cubic integral of motion”, Journal of Physics A: Mathematical and General, 38:4 (2005), 921–927
A. V. Tsiganov, “Isomorphism of the Steklov-Lyapunov system and a potential flow on the surface of a sphere”, Doklady Mathematics, 71:1 (2005), 145–147
2004
111.
A. V. Tsiganov, “Integrable Deformations of Tops Related to the Algebra $so(p,q)$”, Theoret. and Math. Phys., 141:1 (2004), 1348–1360
112.
A. V. Tsiganov, “Toda Chains in the Jacobi Method”, Theoret. and Math. Phys., 139:2 (2004), 636–653
2006
113.
A. V. Tsiganov, “On isomorphism of integrable cases of the Euler equations on the bi-hamiltonian manifolds $e(3)$ and $so(4)$”, J. Math. Sci. (N. Y.), 136:1 (2006), 3641–3647
2004
114.
I. V. Komarov, A. V. Tsiganov, “On integration of the Kowalevski gyrostat and the Clebsch problems”, Regular and Chaotic Dynamics, 9:2 (2004), 169–187
A. V. Tsiganov, O. V. Goremykin, “Integrable systems on so(4) related to XXX spin chains with boundaries”, Journal of Physics A: Mathematical and General, 37:17 (2004), 4843–4849
I. V. Komarov, V. V. Sokolov, A. V. Tsiganov, “Poisson maps and integrable deformations of the Kowalevski top”, Journal of Physics A: Mathematical and General, 36:29 (2003), 8035–8048
V. V. Sokolov, A. V. Tsiganov, “Commutative Poisson Subalgebras for Sklyanin Brackets and Deformations of Some Known Integrable Models”, Theoret. and Math. Phys., 133:3 (2002), 1730–1743
121.
V. V. Sokolov, A. V. Tsiganov, “Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops”, Theoret. and Math. Phys., 131:1 (2002), 543–549
2005
122.
A. V. Tsiganov, “A family of integrable systems on a sphere”, J. Math. Sci. (N. Y.), 125:2 (2005), 249–257
2002
123.
A. V. Tsiganov, “On integrable deformation of the Poincare system”, Regular and Chaotic Dynamics, 7:3 (2002), 331–336
A. V. Tsiganov, “The Maupertuis Principle and Canonical Transformations of the Extended Phase Space”, Journal of Nonlinear Mathematical Physics, 8:1 (2001), 157–182
A. V. Tsiganov, “Properties of the canonical transformations of the time for the Toda lattice and the Henon-Heiles system”, Journal of Physics A: Mathematical and General, 33:26 (2000), 4825–4835
A. V. Tsiganov, “Canonical transformations of the extended phase space, Toda lattices and the Stackel family of integrable systems”, Journal of Physics A: Mathematical and General, 33:22 (2000), 4169–4182
A. V. Tsiganov, “Noncanonical time transformations relating finite-dimensional integrable systems”, Theoret. and Math. Phys., 120:1 (1999), 840–861
138.
A. V. Tsiganov, “Outer automorphisms of $sl(2)$, integrable systems, and mappings”, Theoret. and Math. Phys., 118:2 (1999), 164–172
139.
A. V. Tsiganov, “Lax representation for an integrable motion on the sphere with a qubic second invariant”, Regular and Chaotic Dynamics, 4:3 (1999), 21–29
A. V. Tsiganov, “Automorphisms of sl(2) and classical integrable systems”, Physics Letters, Section A: General, Atomic and Solid State Physics, 251:6 (1999), 354–362
144.
A. V. Tsiganov, “The Stackel systems and algebraic curves”, Journal of Mathematical Physics, 40:1 (1999), 279–298
A. V. Tsiganov, “Superintegrable systems and classical $r$-matrix method”, Theoret. and Math. Phys., 112:3 (1997), 1140–1156
152.
A. V. Tsiganov, “Dynamical r-matrices associated to sl(2) and separation of variables”, International Journal of Modern Physics A, 12:1 (1997), 283–288
153.
A. V. Tsiganov, “The Kowalewski top: A new Lax representation”, Journal of Mathematical Physics, 38:1 (1997), 196–211
S. Rauch-Wojciechowski, A. V. Tsiganov, “Quasi-point separation of variables for the Henon-Heiles system and a system with a quartic potential”, Journal of Physics A: Mathematical and General, 29:23 (1996), 7769–7778
V. B. Kuznetsov, A. V. Tsyganov, “Quantum relativistic Toda lattice”, J. Math. Sci., 80:3 (1996), 1802–1810
156.
A. V. Tsiganov, “The Kowalewski top in SUSY quantum mechanics”, Physics Letters, Section A: General, Atomic and Solid State Physics, 223:1-2 (1996), 63–65
157.
P. P. Kulish, S. Rauch-Wojciechowski, A. V. Tsiganov, “Stationary problems for equation of the KdV type and dynamical r-matrices”, Journal of Mathematical Physics, 37:7 (1996), 3463–3482
J. C. Eilbeck, Enol'skii, V. Z. , V. B. Kuznetsov, A. V. Tsiganov, “Linear r-matrix algebra for classical separable systems”, Journal of Physics A: Mathematical and General, 27:2 (1994), 038, 567–578
V. B. Kuznetsov, A. V. Tsiganov, “Infinite series of Lie algebras and boundary conditions for integrable systems”, J. Soviet Math., 59:5 (1992), 1085–1092
1989
161.
V. B. Kuznetsov, A. V. Tsiganov, “A special case of Neumann's system and the Kowalewski-Chaplygin-Goryachev top”, Journal of Physics A: Mathematical and General, 22:3 (1989), 003, L73–L79
2024
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