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Found 102 Documents (Results 1–100)

Integrable billiards on a Minkowski hyperboloid: extremal polynomials and topology. (English. Russian original) Zbl 07733597

Sb. Math. 213, No. 9, 1187-1221 (2022); translation from Mat. Sb. 213, No. 9, 34-69 (2022).
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Realization of geodesic flows with a linear first integral by billiards with slipping. (English. Russian original) Zbl 1526.37076

Sb. Math. 213, No. 12, 1645-1664 (2022); translation from Mat. Sb. 213, No. 12, 31-52 (2022).
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Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities. (English. Russian original) Zbl 1503.37069

Sb. Math. 213, No. 4, 443-465 (2022); translation from Mat. Sb. 213, No. 4, 3-26 (2022).
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Billiard books realize all bases of Liouville foliations of integrable Hamiltonian systems. (English. Russian original) Zbl 1485.37056

Sb. Math. 212, No. 8, 1122-1179 (2021); translation from Mat. Sb. 212, No. 8, 89-150 (2021).
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Topological classification of Hamiltonian systems on two-dimensional noncompact manifolds. (English. Russian original) Zbl 1456.37062

Sb. Math. 211, No. 8, 1127-1158 (2020); translation from Mat. Sb. 211, No. 8, 68-101 (2020).
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Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems. (English. Russian original) Zbl 1408.37098

Sb. Math. 209, No. 12, 1690-1727 (2018); translation from Mat. Sb. 209, No. 12, 17-56 (2018).
MSC:  37J35 37G10 37J20 70E40 37J05
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Liouville classification of integrable geodesic flows in a potential field on two-dimensional manifolds of revolution: the torus and the Klein bottle. (English. Russian original) Zbl 1408.37097

Sb. Math. 209, No. 11, 1644-1676 (2018); translation from Mat. Sb. 209, No. 11, 103-136 (2018).
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Representation of solutions to the problem of the motion of a heavy rigid body in the Kovalevskaya case in terms of Weierstrass \(\zeta\)- and \(\wp\)-functions and nonintegrability of the Hess case by quadratures. (English. Russian original) Zbl 1401.70007

Sb. Math. 207, No. 7, 889-914 (2016); translation from Mat. Sb. 207, No. 7, 3-28 (2016).
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Topology of the configuration space, singularities of the potential, and polynomial integrals of equations of dynamics. (English. Russian original) Zbl 1403.70009

Sb. Math. 207, No. 10, 1435-1449 (2016); translation from Mat. Sb. 207, No. 10, 80-95 (2016).
MSC:  70G40 37D50 37J35 70G10 70H06 70H07
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Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field. (English. Russian original) Zbl 1316.70006

Sb. Math. 203, No. 2, 257-287 (2012); translation from Mat. Sb. 203, No. 2, 111-142 (2012).
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Classification of nondegenerate equilibria and degenerate 1-dimensional orbits of the Kovalevskaya-Yehia integrable system. (English. Russian original) Zbl 1253.37056

Sb. Math. 203, No. 1, 28-59 (2012); translation from Mat. Sb. 203, No. 1, 31-60 (2012).
MSC:  37J35 70E05 70E40 37J05
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The topology of Lagrangian foliations of integrable systems with hyperelliptic Hamiltonian. (English. Russian original) Zbl 1242.37036

Sb. Math. 202, No. 3, 373-411 (2011); translation from Mat. Sb. 2011, No. 3, 69-106 (2011).
MSC:  37J05 37J35
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Bifurcation diagram and the discriminant of a spectral curve of integrable systems on Lie algebras. (English. Russian original) Zbl 1230.37074

Sb. Math. 201, No. 9, 1273-1305 (2010); translation from Mat. Sb. 201, No. 9, 27-60 (2010).
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Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems. (English. Russian original) Zbl 1205.37072

Sb. Math. 201, No. 8, 1153-1191 (2010); translation from Mat. Sb. 201, No. 8, 63-102 (2010).
MSC:  37J35 37J05 37J15 57R45 58K45 70G40
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The topology of Liouville foliation for the Sokolov integrable case on the Lie algebra so(4). (English. Russian original) Zbl 1179.37079

Sb. Math. 200, No. 6, 899-921 (2009); translation from Mat. Sb. 200, No. 6, 119-142 (2009).
MSC:  37J35 70H06
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Maximally symmetric cell decompositions of surfaces and their coverings. (English. Russian original) Zbl 1163.37018

Sb. Math. 199, No. 9, 1263-1353 (2008); translation from Mat. Sb. 199, No. 9, 3-96 (2008).
MSC:  37J35 57M20 57M12 70H06
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Approximation properties of the poles of diagonal Padé approximants for certain generalizations of Markov functions. (English. Russian original) Zbl 1064.30035

Sb. Math. 193, No. 12, 1837-1866 (2002); translation from Mat. Sb. 193, No. 12, 105-133 (2002).
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Polynomial integrals of reversible mechanical systems with a two-dimensional torus as the configuration space. (English. Russian original) Zbl 0964.70015

Sb. Math. 191, No. 2, 189-208 (2000); translation from Mat. Sb. 191, No. 2, 43-63 (2000).
MSC:  70H06 70G10
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Deformations of non-compact complex curves and envelopes of meromorphy of spheres. (English. Russian original) Zbl 0920.32012

Sb. Math. 189, No. 9, 1295-1333 (1998); translation from Mat. Sb. 189, No. 9, 23-60 (1998).
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Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry. (English. Russian original) Zbl 0917.58031

Sb. Math. 189, No. 10, 1441-1466 (1998); translation from Mat. Sb. 189, No. 10, 5-32 (1998).
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Integrable Hamiltonian systems with two degrees of freedom. The topological structure of saturated neighbourhoods of points of focus-focus and saddle-saddle type. (English. Russian original) Zbl 0871.58045

Sb. Math. 187, No. 4, 495-524 (1996); translation from Mat. Sb. 187, No. 4, 29-58 (1996).
MSC:  37J99 54H20 37G99 37C85 37G15 70G10
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Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of \(\mathbb{R}^ 2\) in extended neighbourhoods of simple singular points. III: Realization. (English. Russian original) Zbl 0865.58020

Sb. Math. 186, No. 10, 1477-1491 (1995); translation from Mat. Sb. 186, No. 10, 89-102 (1995).
MSC:  37J99 37G99 37G15
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