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Lokutsievskiy Lev Vyacheslavovich
(recent publications)

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scientific publications

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Articles


2023
1.	L. V. Lokutsievskiy, A. I. Ovseevich, “Asymptotic control theory for a closed string II”, Optimal Control and Dynamical Systems, Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovic Gamkrelidze, Trudy Mat. Inst. Steklova, 321, Steklov Math. Inst., Moscow, 2023 (to appear)

2022
2.	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
3.	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)
4.	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)
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 $https://adsabs.harvard.edu/cgi-bin/bib_query?{https://adsabs.harvard.edu/cgi-bin/bib_query?=> NASA Identifier determination: (lokutsievskiy 2021 Russian Mathematical Surveys 76 936-938 ) adsres.cfa.harvard.edu/cgi-bin/refcgi.py?resolvethose=lokutsievskiy Warning: fsockopen(): unable to connect to adsres.cfa.harvard.edu:80 (Connection timed out) in /data1/home/http/MATHNET/include/HREFS/getADSNASAHrefs.inc on line 20 => Connection failed}$
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)

2018
13.	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)
14.	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)

2017
15.	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)
16.	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)
17.	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)
18.	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
19.	L. V. Lokutsievskiy, “On an optimal flow in a class of nilpotent convex problems”, Proc. Steklov Inst. Math., 291 (2015), 146–169 (cited: 1)
20.	Lev Lokutsievskiy, Vincent Runge, “Optimal control by multipoles in the Hele-Shaw problem”, J. Math. Fluid Mech., 17:2 (2015), 261–277

2014
21.	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)
22.	L. V. Lokutsievskii, “Generic structure of the Lagrangian manifold in chattering problems”, Math. Notes, 95:6 (2014), 786–794
23.	L. V. Lokutsievskii, “The Hamiltonian property of the flow of singular trajectories”, Sb. Math., 205:3 (2014), 432–458 (cited: 2)

2013
24.	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)
25.	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)
26.	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
27.	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)
28.	L. V. Lokutsievskiy, “Fractal structure of hyperbolic Lipschitzian dynamical system”, Russ. J. Math. Phys., 19:1 (2012), 27–44 (cited: 3) (cited: 4)

2011
29.	L. V. Lokutsievskiy, “Optimal probabilistic search”, Sb. Math., 202:5 (2011), 697–719 (cited: 3) (cited: 1)
30.	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)
Proceedings


2019
31.	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
32.	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
Popular science or education materials


2018
33.	L. V. Lokutsievskiy, V. M. Tikhomirov, Kvant, 2018, no. 6, 11–17
34.	L. V. Lokutsievskiy, V. M. Tikhomirov, Kvant, 2018, no. 5, 2–8
Miscellaneous


2023
35.	Optimalnoe upravlenie i dinamicheskie sistemy, Sbornik statei. K 95-letiyu akademika Revaza Valerianovicha Gamkrelidze, Trudy MIAN, 321, ed. A. A. Agrachev, L. V. Lokutsievskii, A. V. Sarychev, Yu. L. Sachkov, MIAN, M., 2023

2021
36.	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. ; ; ; ;

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