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Found 148 Documents (Results 1–100)

Dynamics of systems with unilateral differential constraints. (English. Russian original) Zbl 07820589

Dokl. Math. 108, No. 3, 431-437 (2023); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 514, 12-19 (2023).
MSC:  70F25 70H03
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Averaged spatial circular restricted three-body problem: internal case and new results. (English. Russian original) Zbl 07786641

Dokl. Math. 108, No. 1, 269-276 (2023); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 512, 33-41 (2023).
MSC:  70F07 70K65 70-08
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Extremum conditions for constrained scalar control of two nonsynchronous oscillators in the time-optimal control problem. (English. Russian original) Zbl 1498.49039

Dokl. Math. 106, No. 1, 286-290 (2022); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 505, 86-91 (2022).
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On derivation of equations of electrodynamics and gravitation from the principle of least action, the Hamilton-Jacobi method, and cosmological solutions. (English. Russian original) Zbl 1507.83012

Dokl. Math. 105, No. 3, 178-182 (2022); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 504, 51-55 (2022).
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Existence and stability of equilibrium solutions of the Vlasov equation with a modified gravitational potential. (English. Russian original) Zbl 1487.81139

Dokl. Math. 104, No. 2, 277-281 (2021); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 500, 67-73 (2021).
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New cases of homogeneous integrable systems with dissipation on tangent bundles of four-dimensional manifolds. (English. Russian original) Zbl 1482.37059

Dokl. Math. 103, No. 2, 85-91 (2021); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 497, 23-30 (2021).
MSC:  37J35 37J39 70H06
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Force evolutionary billiards and billiard equivalence of the Euler and Lagrange cases. (English. Russian original) Zbl 1482.37060

Dokl. Math. 103, No. 1, 1-4 (2021); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 496, 5-8 (2021).
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New cases of homogeneous integrable systems with dissipation on tangent bundles of three-dimensional manifolds. (English. Russian original) Zbl 1482.37058

Dokl. Math. 102, No. 3, 518-523 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 495, 84-90 (2020).
MSC:  37J35 37J39 70H06
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On the existence of focus singularities in one model of a Lagrange top with a vibrating suspension point. (English. Russian original) Zbl 1482.37054

Dokl. Math. 102, No. 3, 468-471 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 495, 26-30 (2020).
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New cases of homogeneous integrable systems with dissipation on tangent bundles of two-dimensional manifolds. (English. Russian original) Zbl 1482.37057

Dokl. Math. 102, No. 2, 443-448 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 494, 105-111 (2020).
MSC:  37J35 37J39 70H06
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Reducing the degree of integrals of Hamiltonian systems by using billiards. (English. Russian original) Zbl 1423.37055

Dokl. Math. 99, No. 3, 266-269 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 486, No. 2, 151-155 (2019).
MSC:  37J35 37D50 70E40
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Bifurcations of Liouville tori in a system of two vortices of positive intensity in a Bose-Einstein condensate. (English. Russian original) Zbl 1416.37052

Dokl. Math. 99, No. 2, 225-229 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 485, No. 6, 670-675 (2019).
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Hamiltonian approach to secondary quantization. (English. Russian original) Zbl 1410.81029

Dokl. Math. 98, No. 3, 571-574 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 483, No. 2, 138-142 (2018).
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Bifurcation diagram of the two vortices in a Bose-Einstein condensate with intensities of the same signs. (English. Russian original) Zbl 1396.37063

Dokl. Math. 97, No. 3, 286-290 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 480, No. 6, 652-656 (2018).
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On the stability of a periodic Hamiltonian system with one degree of freedom in a transcendental case. (English. Russian original) Zbl 1436.70006

Dokl. Math. 97, No. 2, 161-163 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 479, No. 5, 485-488 (2018).
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Instability degree and singular subspaces of integral isotropic cones of linear systems of differential equations. (English. Russian original) Zbl 1430.34066

Dokl. Math. 97, No. 1, 35-37 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 478, No. 3, 259-261 (2018).
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Integrable billiards model important integrable cases of rigid body dynamics. (English. Russian original) Zbl 1335.37040

Dokl. Math. 92, No. 3, 682-684 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 465, No. 2, 150-153 (2015).
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Cascade of bifurcations in Lorenz-like systems: birth of a strange attractor, blue sky catastrophe bifurcation, and nine homoclinic bifurcations. (English. Russian original) Zbl 1360.37133

Dokl. Math. 92, No. 2, 563-567 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 464, No. 4, 391-395 (2015).
MSC:  37G35 70K50 37G15
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Wigner quantization of Hamilton-Dirac systems. (English. Russian original) Zbl 1337.81082

Dokl. Math. 91, No. 1, 114-116 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 460, No. 5, 525-528 (2015).
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Hamiltonian structures in the quantum theory of Hamilton-Dirac systems. (English. Russian original) Zbl 1337.81086

Dokl. Math. 91, No. 1, 68-71 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 460, No. 4, 385-388 (2015).
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Exponential convergence of multi-dimensional stochastic mechanical systems with switching impacts. (English. Russian original) Zbl 1330.60071

Dokl. Math. 91, No. 1, 60-63 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 460, No. 4, 377-380 (2015).
MSC:  60H10 70F99
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Coordinate uncertainty principle in a generalized phase space. (English. Russian original) Zbl 1317.82048

Dokl. Math. 90, No. 2, 628-630 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 458, No. 2, 150-152 (2014).
MSC:  82C40 70B05
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Regular attractors of autonomous and nonautonomous dynamical systems. (English) Zbl 1307.37012

Dokl. Math. 89, No. 1, 92-97 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 454, No. 5, 512-517 (2014).
MSC:  37C60 37C70 70K60
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On infinite-dimensional Lagrangian systems with nonpotential forces. (English. Russian original) Zbl 1294.70011

Dokl. Math. 87, No. 1, 110-111 (2013); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 448, No. 5, 518-519 (2013).
MSC:  70H03 37N05 37K99
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Bifurcation diagram for the Kovalevskaya case on the Lie algebra \(\mathrm{so}(4)\). (English. Russian summary) Zbl 1268.37076

Dokl. Math. 86, No. 3, 827-830 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 447, No. 5, 486-489 (2012).
MSC:  37J15 37J20 37J35 70H06
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Asymptotic behavior of solutions of differential equations describing synchronous machines. (English. Russian original) Zbl 1348.70054

Dokl. Math. 86, No. 1, 530-533 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 445, No. 4, 386-389 (2012).
MSC:  70K20 34D05
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Optimization of the boundary control of string vibrations at one string end with a given mode at the other end. (English. Russian original) Zbl 1263.93102

Dokl. Math. 86, No. 1, 454-456 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 445, No. 1, 13-16 (2012).
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Optimization scheme for boundary control by displacements at two ends of oscillations of a rod consisting of two dissimilar segments. (English. Russian original) Zbl 1264.93085

Dokl. Math. 84, No. 3, 854-856 (2011); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 441, No. 6, 731-733 (2011).
MSC:  93C15 70Q05 49J15
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A mathematical model for the angular motion of large space structures with gyroscopic drive for an active compensation of elastic oscillations. (English. Russian original) Zbl 1358.70035

Dokl. Math. 83, No. 1, 136-139 (2011); translation from Dokl. Akad. Nauk 436, No. 6, 743-746 (2011).
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Mixed problems for the telegraph equation in the case of a system consisting of two segments with different densities and elasticities but equal impedances: one-sided control. (English. Russian original) Zbl 1215.93068

Dokl. Math. 82, No. 3, 858-861 (2010); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 435, No. 1, 22-25 (2010).
MSC:  93C20 35L20 70Q05
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Homoclinic orbits to 1-elliptic points and KAM-curves and scattering. (English. Russian original) Zbl 1208.37015

Dokl. Math. 82, No. 1, 508-510 (2010); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 433, No. 1, 10-12 (2010).
MSC:  37C29 70H08 70H05
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On the bi-Hamiltonian structure of the Goryachev system on the sphere. (English. Russian original) Zbl 1181.37102

Dokl. Math. 79, No. 3, 430-433 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 426, No. 6, 740-743 (2009).
MSC:  37K10 70H20 70H06
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Symmetries and first integrals in the mechanics of infinite-dimensional systems. (English. Russian original) Zbl 1347.70025

Dokl. Math. 79, No. 2, 189-190 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 425, No. 2, 169-171 (2009).
MSC:  70G60 70G65 70G70 37K05 34G20 35A30
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Gyroscopic stabilization of degenerate equilibria and the topology of real algebraic varieties. (English. Russian original) Zbl 1152.37022

Dokl. Math. 77, No. 3, 412-415 (2008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 420, No. 4, 447-450 (2008).
MSC:  37J05 70E05 14P25 14H70
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Gyroscopic stabilization in the presence of nonconservative forces. (English. Russian original) Zbl 1179.70010

Dokl. Math. 76, No. 2, 780-785 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 416, No. 4, 451-456 (2007).
MSC:  70J25 34D20 70Q05
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Homoclinic orbits for invariant tori of nearly integrable Hamiltonian systems. (English. Russian original) Zbl 1327.37018

Dokl. Math. 73, No. 2, 217-220 (2006); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 407, No. 3, 307-310 (2006).
MSC:  37J40 37C29 70H08
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Estimation of the sojourn time of a weakly perturbed Lagrangian system in a given region. (English. Russian original) Zbl 1378.93115

Dokl. Math. 74, No. 3, 930-933 (2006); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 411, No. 1, 25-29 (2006).
MSC:  93E03 34F05 34C29 37J05 37N35 62G05 70H03
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Optimization of a boundary control by a displacement at one end of a string based on minimization of the integral of the modulus of the derivative of the displacement raised to an arbitrary power \(p \geq 1\). (English. Russian original) Zbl 1204.49017

Dokl. Math. 74, No. 3, 878-882 (2006); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 411, No. 6, 736-740 (2006).
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Series of rational potentials separable in elliptic coordinates. (English. Russian original) Zbl 1208.37028

Dokl. Math. 74, No. 3, 834-838 (2006); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 411, No. 3, 309-313 (2006).
MSC:  37F10 70H20 70H06
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Simple exact solutions to the N. Kowalewski equations. (English. Russian original) Zbl 1160.70004

Dokl. Math. 74, No. 1, 536-539 (2006); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 409, No. 4, 439-440 (2006).
MSC:  70E40 70E17
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Instability of distributed nonconservative systems caused by weak dissipation. (English. Russian original) Zbl 1272.70082

Dokl. Math. 71, No. 3, 470-475 (2005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 402, No. 4, 460-466 (2005).
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The topology of isoenergetic surfaces for the Sokolov integrable case in the Lie algebra \(\mathrm{so}(4)\). (English. Russian original) Zbl 1272.37028

Dokl. Math. 71, No. 2, 256-259 (2005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 401, No. 5, 599-602 (2005).
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Necessary and sufficient conditions for the polynomial integrability of generalized Toda chains. (English. Russian original) Zbl 1122.37316

Dokl. Math. 69, No. 1, 131-135 (2004); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 394, No. 4, 449-453 (2004).
MSC:  37J35 70H06
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On reductions on groups of geodesic flows with (left-) right-invariant metrics and their fields of symmetry. (English. Russian original) Zbl 1123.37316

Dokl. Math. 68, No. 1, 75-78 (2003); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 391, No. 4, 439-442 (2003).
MSC:  37J35 37J15 37K65 70E40 70H33 37N10
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Splitting of asymptotic manifolds in some Hamiltonian systems with two degrees of freedom. (English. Russian original) Zbl 1246.70018

Dokl. Math. 67, No. 1, 47-49 (2003); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 388, No. 4, 452-455 (2003).
MSC:  70H09 37J40 37J45
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