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Lokutsievskiy Lev Vyacheslavovich
(recent publications)

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2022
1.	Lev Lokutsievskiy, Gerd Wachsmuth, Mikhail Zelikin, “Non-optimality of conical parts for Newton’s problem of minimal resistance in the class of convex bodies and the limiting case of infinite height”, Calc. Var. Partial Differential Equations, 61:1 (2022), 31 , 18 pp. ;

2021
2.	L. V. Lokutsievskiy, “Explicit Formulae for Geodesics in Left–Invariant Sub–Finsler Problems on Heisenberg Groups via Convex Trigonometry”, J. Dyn. Control Syst., 27 (2021), 661–681 (cited: 1) (cited: 1)
3.	A. A. Ardentov, L. V. Lokutsievskiy, Yu. L. Sachkov, “Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry”, ESAIM: COCV, 27 (2021), 32 , 52 pp., arXiv: 2004.10194 (cited: 1) (cited: 1);
4.	Optimalnoe upravlenie i differentsialnye igry, Sbornik statei, Trudy MIAN, 315, ed. S. M. Aseev, L. V. Lokutsievskii, M. S. Nikolskii, MIAN, M., 2021 , 304 pp.
5.	M. I. Ronzhina, L. A. Manita, L. V. Lokutsievskiy, “Neighborhood of the Second-Order Singular Regime in Problems with Control in a Disk”, Proc. Steklov Inst. Math., 315 (2021), 209–222
6.	Lev Lokutsievskiy, Alexander Pechen, “Reachable sets for two-level open quantum systems driven by coherent and incoherent controls”, Journal of Physics A: Mathematical and Theoretical, 54:39 (2021), 395304 , 20 pp., arXiv: 2109.04384 (cited: 1) (cited: 1)
7.	M. I. Ronzhina, L. A. Manita, L. V. Lokutsievskiy, “Solutions of a Hamiltonian system with two-dimensional control in a neighbourhood of a singular second-order extremal”, Russian Math. Surveys, 76:5 (2021), 936–938
8.	Alexey I. Kushnir, Lev V. Lokutsievskiy, “When is a monotone function cyclically monotone?”, Theor. Econ., 16:3 (2021), 853–879 (cited: 1) ;

2020
9.	L. V. Lokutsievskiy, M. I. Zelikin, “The analytical solution of Newton’s aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary”, ESAIM: COCV, 26 (2020), 15 , 36 pp., arXiv: 1905.02028 (cited: 2) (cited: 2);
10.	A. A. Ardentov, L. V. Lokutsievskiy, Yu. L. Sachkov, “Explicit solutions for a series of optimization problems with 2-dimensional control via convex trigonometry”, Dokl. Math., 102 (2020), 427–432 (cited: 1) (cited: 1)

2019
11.	L. V. Lokoutsievskiy, V. A. Myrikova, “Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set”, Math. Notes, 105:1 (2019), 36–55 (cited: 1) (cited: 1)
12.	L. V. Lokutsievskiy, “Convex trigonometry with applications to sub-Finsler geometry”, Sb. Math., 210:8 (2019), 1179–1205 (cited: 7) (cited: 9)
13.	M. I. Zelikin, L. V. Lokutsievskiy, “Analytical solution of Newton's aerodynamic problem without the assumption of rotational symmetry”, Materialy Mezhdunarodnoi konferentsii "Ustoichivost, upravlenie, differentsialnye igry (SCDG2019)", posvyaschennoi 95-letiyu so dnya rozhdeniya akademika N.N. Krasovskogo (Ekaterinburg, 16–20 sentyabrya 2019 g.), IMM UrO RAN, 2019, 464 , arXiv: 1905.02028
14.	Lev V. Lokutsievskiy, “Convex trigonometry with applications to sub-Finsler geometry”, Materialy Mezhdunarodnoi konferentsii "Ustoichivost, upravlenie, differentsialnye igry (SCDG2019)", posvyaschennoi 95-letiyu so dnya rozhdeniya akademika N.N. Krasovskogo (Ekaterinburg, 16–20 sentyabrya 2019 g.), Institut matematiki i mekhaniki UrO RAN im. N.N. Krasovskogo, 2019, 435–436 , arXiv: 1807.08155

2018
15.	L. V. Lokutsievskiy, Yu. L. Sachkov, “Liouville integrability of sub-Riemannian problems on Carnot groups of step 4 or greater”, Sb. Math., 209:5 (2018), 672–713 (cited: 9) (cited: 11)
16.	L. V. Lokutsievskiy, M. I. Zelikin, “Hessian measures in the aerodynamic Newton problem”, J. Dyn. Control Syst., 24:3 (2018), 475–495 (cited: 3) (cited: 3)
17.	L. V. Lokutsievskiy, V. M. Tikhomirov, Kvant, 2018, no. 6, 11–17
18.	L. V. Lokutsievskiy, V. M. Tikhomirov, Kvant, 2018, no. 5, 2–8

2017
19.	A.V. Arutyunov, A.V. Greshnov, L.V. Lokutsievskii, K.V. Storozhuk, “Topological and geometrical properties of spaces with symmetric and nonsymmetric $f$-quasimetrics”, Topology Appl., 221 (2017), 178–194 (cited: 16) (cited: 19)
20.	M. I. Zelikin, L. V. Lokutsievskiy, S. V. Skopintcev, “On Optimal Harvesting of a Resource on a Circle”, Math. Notes, 102:4 (2017), 521–532 (cited: 3) (cited: 3)
21.	L. V. Lokutsievskiy, Yu. L. Sachkov, “Liouville nonintegrability of sub-Riemannian problems on free Carnot groups of step 4”, Dokl. Math., 95:3 (2017), 211–213 (cited: 2) (cited: 2)
22.	M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand, “Typicality of Chaotic Fractal Behavior of Integral Vortices in Hamiltonian Systems with Discontinuous Right Hand Side”, Journal of Mathematical Sciences, 221:1 (2017), 1-136 , arXiv: 1506.02320 (cited: 6)

2015
23.	L. V. Lokutsievskiy, “On an optimal flow in a class of nilpotent convex problems”, Proc. Steklov Inst. Math., 291 (2015), 146–169 (cited: 1)
24.	Lev Lokutsievskiy, Vincent Runge, “Optimal control by multipoles in the Hele-Shaw problem”, J. Math. Fluid Mech., 17:2 (2015), 261–277

2014
25.	L. V. Lokutsievskii, “Singular regimes in controlled systems with multidimensional control in a polyhedron.”, Izv. Math., 78:5 (2014), 1006–1027 (cited: 3) (cited: 1) (cited: 1) (cited: 2)
26.	L. V. Lokutsievskii, “Generic structure of the Lagrangian manifold in chattering problems”, Math. Notes, 95:6 (2014), 786–794
27.	L. V. Lokutsievskii, “The Hamiltonian property of the flow of singular trajectories”, Sb. Math., 205:3 (2014), 432–458 (cited: 2)

2013
28.	M. I. Zelikin, D. D. Kiselev, L. V. Lokutsievskii, “Optimal control and Galois theory”, Sb. Math., 204:11 (2013), 1624–1638 (cited: 3) (cited: 1) (cited: 1) (cited: 4)
29.	R. Hildebrand,L. V. Lokutsievskiy, M. I. Zelikin, “Generic Fractal Structure of Finite Parts of Trajectories of Piecewise Smooth Hamiltonian Systems”, Russ. J. Math. Phys., 20:1 (2013), 25–32 (cited: 3) (cited: 4)
30.	M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand, “Stochastic dynamics of lie algebras of Poisson brackets in neighborhoods of nonsmoothness points of Hamiltonians”, Dokl. Math., 87:3 (2013), 259–263 (cited: 1)

2012
31.	M. I. Zelikin, L. V. Lokutsievskiy, R. Hildebrand, “Geometry of neighborhoods of singular trajectories in problems with multidimensional control”, Proc. Steklov Inst. Math., 277 (2012), 67–83 (cited: 12) (cited: 4) (cited: 4) (cited: 6)
32.	L. V. Lokutsievskiy, “Fractal structure of hyperbolic Lipschitzian dynamical system”, Russ. J. Math. Phys., 19:1 (2012), 27–44 (cited: 3) (cited: 4)

2011
33.	L. V. Lokutsievskiy, “Optimal probabilistic search”, Sb. Math., 202:5 (2011), 697–719 (cited: 3) (cited: 1)
34.	L. V. Lokutsievskii, “Homotopy classification of actions of finite groups on aspherical spaces”, J. Math. Sci., 177:2 (2011), 244-256 (cited: 1) (cited: 1)

Full list of publications