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Zelikin Mikhail Il'ich
(full list of publications)
| by years | scientific publications | by types |


1. L. V. Lokutsievskiy, M. I. Zelikin, “Hessian measures in the aerodynamic Newton problem”, J. Dyn. Control Syst., 2018, 1–21 (Published online)  mathnet  crossref  isi  scopus
2. M. I. Zelikin, “Genius. In the Memory of I. Shafarevich”, Math. Ed., 2018, no. 1(85), 2–4  mathnet

3. M. I. Zelikin, L. V. Lokoutsievskiy, S. V. Skopintcev, “On Optimal Harvesting of a Resource on a Circle”, Math. Notes, 102:4 (2017), 521–532  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
4. M. I. Zelikin, “An analogue of Pontryagin's maximum principle in problems of minimization of multiple integrals”, Izv. Math., 81:5 (2017), 973–984  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  scopus
5. 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  mathnet  crossref

6. M. I. Zelikin, “Fractal Theory of Saturn's Ring”, Proc. Steklov Inst. Math., 291 (2015), 87–101  mathnet  crossref  crossref  isi  elib  scopus

7. M. I. Zelikin, D. D. Kiselev, L. V. Lokutsievskii, “Optimal control and Galois theory”, Sb. Math., 204:11 (2013), 1624–1638  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 3)
8. 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  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 1)
9. R. Hildebrand, L. V. Lokoutsievskiy, 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  mathnet  crossref  mathscinet  zmath  isi (cited: 3)  scopus (cited: 4)

10. V. F. Borisov, V. V. Gael, M. I. Zelikin, “Chattering regimes and Lagrangian manifolds in problems with phase constraints”, Izv. Math., 76:1 (2012), 1–38  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
11. M. I. Zelikin, “Theory and applications of the problem of Euler elastica”, Russian Math. Surveys, 67:2 (2012), 281–296  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 3)
12. 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  mathnet  crossref  mathscinet  zmath  isi (cited: 8)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 3)
13. Yu. S. Osipov, M. I. Zelikin, “Higher-order elastics and elastic hulls”, Russ. J. Math. Phys., 19:2 (2012), 234–243  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 2)
14. Yu. S. Osipov, M. I. Zelikin, “Multidimensional generalizations of Jacobi's envelope theorem”, Russ. J. Math. Phys., 19:1 (2012), 101–106  mathnet  crossref  mathscinet  zmath  isi  scopus

15. M. I. Zelikin, “Theory of fields of extremals for multiple integrals”, Russian Math. Surveys, 66:4 (2011), 733–765  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib  elib  scopus

16. V. F. Borisov, M. I. Zelikin, L. A. Manita, “Optimal synthesis in an infinite-dimensional space”, Proc. Steklov Inst. Math., 271 (2010), 34–52  mathnet  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus (cited: 2)
17. M. I. Zelikin, V. F. Borisov, “Geometry of extremals with a countable number of contact points with the boundary of the phase constraint”, Dokl. Akad. Nauk, 430:1 (2010), 7–12  mathscinet  zmath

18. M. I. Zelikin, “A criterion for the symmetry of a spectrum”, Dokl. Akad. Nauk, 418:6 (2008), 737–740  mathnet  mathscinet (cited: 1)

19. V. F. Borisov, M. I. Zelikin, L. A. Manita, “Extremals with accumulation of switchings in infinite-dimensional spaces”, J. Math. Sci., 160:2 (2009), 139–196  crossref  mathscinet  zmath  elib (cited: 1)  scopus (cited: 1)
20. M. I. Zelikin, L. V. Lokutsievskii, R. A. Usachev, “Vortex singularities of optimal strategies in search games”, J. Math. Sci., 160:2 (2009), 197–220  crossref  mathscinet  zmath  elib  scopus

21. J. Appl. Math. Mech., 70:2 (2006), 264–273  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 2)

22. M. I. Zelikin, L. A. Manita, “Accumulation of Switchings in Distributed Parameter Problems”, Journal of Mathematical Sciences, 151:6 (2008), 3506–3542  mathnet  crossref  mathscinet  zmath  scopus
23. M. I. Zelikin, “Superconductivity of Plasma and Fireballs”, Journal of Mathematical Sciences, 151:6 (2008), 3473–3496  mathnet  crossref  zmath  elib (cited: 5)  scopus (cited: 5)

24. M. I. Zelikin, N. B. Melnikov, “The Bellman function and optimal synthesis in control problems with nonsmooth constraints”, J. Math. Sci. (N. Y.), 121:2 (2004), 2281–2294  mathnet  crossref  mathscinet  zmath
25. M. I. Zelikin, “Optimal problems on Hölder function spaces”, J. Math. Sci. (N. Y.), 121:2 (2004), 2265–2280  mathnet  crossref  mathscinet  zmath

26. M. I. Zelikin, “Geometry of operator cross ratio”, Sb. Math., 197:1 (2006), 37–51  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)

27. M. I. Zelikin, “An efficient criterion for optimality in terms of two solutions of the Riccati equation”, Dokl. Akad. Nauk, 397:3 (2004), 300–303  mathnet  mathscinet  scopus
28. J. Appl. Math. Mech., 68:4 (2004), 617–622  crossref  mathscinet  zmath  isi  scopus  scopus
29. M. I. Zelikin, “Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems”, Sb. Math., 195:6 (2004), 819–831  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 4)

30. M. I. Zelikin, V. F. Borisov, “Singular optimal regimes in problems of mathematical economics”, J. Math. Sci. (N. Y.), 130:1 (2005), 4409–4570  crossref  mathscinet  zmath  scopus (cited: 8)

31. M. I. Zelikin, “Hölderian extremal problems”, Patterns and waves (Saint Petersburg, 2002), AkademPrint, St. Petersburg, 2003, 412–432  mathscinet
32. M. I. Zelikin, “The $\zeta$-function of the cross-ratio on Sato's Grassmannian as an integral invariant of the Kadomtsev-Petviashvili hierarchy”, Dokl. Akad. Nauk, 389:2 (2003), 159–163  mathnet (cited: 1)  mathscinet (cited: 2)  zmath
33. M. I. Zelikin, V. F. Borisov, “Optimal chattering feedback control”, J. Math. Sci. (N. Y.), 114:3 (2003), 1227–1344  mathnet  crossref  mathscinet  zmath

34. M. I. Zelikin, “Chattering on optimal trajectories of Hölder problems”, Sb. Math., 193:5 (2002), 669–683  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
35. M. I. Zelikin, “The Structure of Optimal Synthesis in the Vicinity of Singular Manifolds for Problems Affine with Respect to Control”, Proc. Steklov Inst. Math., 236 (2002), 164–185  mathnet  mathscinet  zmath

36. Differ. Equ., 37:9 (2001), 1217–1223  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
37. M. I. Zelikin, “Optimal control in Hölder classes of functions”, Dokl. Akad. Nauk, 378:6 (2001), 733–736  mathnet  mathscinet  zmath
38. M. I. Zelikin, N. B. Melnikov, R. Hildebrand, “The Topological Structure of the Phase Portrait of a Typical Fiber of Optimal Synthesis for Chattering Problems”, Proc. Steklov Inst. Math., 233 (2001), 116–142  mathnet  mathscinet  zmath
39. M. I. Zelikin, L. F. Zelikina, R. Hildebrand, “Asymptotics of Optimal Synthesis for One Class of Extremal Problems”, Proc. Steklov Inst. Math., 233 (2001), 87–115  mathnet  mathscinet  zmath
40. M. I. Zelikin, “Synthesis of Optimal Trajectories That Defines the Reeb Foliation”, Proc. Steklov Inst. Math., 233 (2001), 81–86  mathnet  mathscinet  zmath

41. V. F. Borisov, M. I. Zelikin, “Approaching the intermediate thrust modes in control problems of space navigation”, Russ. J. Math. Phys., 7:2 (2000), 127–146  mathscinet  zmath  isi  scopus
42. M. I. Zelikin, “To the theory of chattering control”, Spectral and evolution problems (Sevastopol', 1999), Vol. 10, Natl. Taurida Univ. “V. Vernadsky”, Simferopol', 2000, 170–172  mathscinet

43. Differential Equations, 35:11 (1999), 1489–1493 (2000)  mathnet  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
44. M. I. Zelikin, “The asymptotics of the deviation of a functional from its optimal value when chattering is replaced by a suboptimal regime”, Russian Math. Surveys, 54:3 (1999), 662–664  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  scopus
45. M. I. Zelikin, L. F. Zelikina, “Exact Constants in Kolmogorov-Type Inequalities”, Proc. Steklov Inst. Math., 227 (1999), 131–139  mathnet  mathscinet  zmath
46. M. I. Zelikin, “Optimal Synthesis Containing Successively Inserted Chattering Bundles”, Proc. Steklov Inst. Math., 224 (1999), 137–148  mathnet  mathscinet  zmath

47. M. I. Zelikin, “Cartan–Siegel homogeneous domains as integral manifolds of the complex Riccati-type equation”, Proc. Steklov Inst. Math., 220 (1998), 126–137  mathnet  mathscinet  zmath
48. M. I. Zelikin, “A quadratic system of partial differential equations that is associated with the problem of minimizing a multiple integral”, Dokl. Akad. Nauk, 358:1 (1998), 7–9  mathnet  mathscinet  zmath  isi  scopus
49. M. I. Zelikin, L. F. Zelikina, “The structure of optimal synthesis in a neighbourhood of singular manifolds for problems that are affine in control”, Sb. Math., 189:10 (1998), 1467–1484  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)

50. M. I. Zelikin, “One-parameter families of solutions to a class of PDE optimal control problems”, Optimization methods in partial differential equations (South Hadley, MA, 1996), Contemp. Math., 209, Amer. Math. Soc., Providence, RI, 1997, 339–349  crossref  mathscinet (cited: 3)  zmath
51. M. I. Zelikin, “On the connection generated by the problem of minimizing a multiple integral”, Sb. Math., 188:1 (1997), 61–74  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus

52. M. I. Zelikin, “The Fuller phenomenon in problems of vibration of two linked oscillators”, Dynamical systems, 1, J. Math. Sci., 78:5 (1996), 626–631  crossref  mathscinet (cited: 3)  zmath  scopus (cited: 3)

53. M. I. Zelikin, “Totally extremal manifolds for optimal control problems”, Semigroups in algebra, geometry and analysis (Oberwolfach, 1993), de Gruyter Exp. Math., 20, de Gruyter, Berlin, 1995, 339–354  mathscinet (cited: 1)  zmath
54. M. I. Zelikin, “Irregularity of optimal control in regular extremal problems”, Fundam. Prikl. Mat., 1:2 (1995), 399–408  mathnet  mathscinet  zmath

55. M. I. Zelikin, “On the theory of the matrix Riccati equation. II”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 213–230  mathnet  crossref  mathscinet  zmath  adsnasa  isi

56. M. I. Zelikin, V. F. Borisov, “Regimes with frequented switches in the problems of optimal control”, Proc. Steklov Inst. Math., 197 (1993), 95–186  mathnet  mathscinet  zmath

57. M. I. Zelikin, V. F. Borosov, “Optimal synthesis containing chattering arcs and singular arcs of the second order”, Nonlinear synthesis (Sopron, 1989), Progr. Systems Control Theory, 9, Birkhäuser Boston, Boston, MA, 1991, 283–296  mathscinet (cited: 1)

58. M. I. Zelikin, “On the theory of the matrix Riccati equation”, Math. USSR-Sb., 73:2 (1992), 341–354  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)

59. M. I. Zelikin, V. F. Borisov, “Synthesis in problems of optimal control containing trajectories with participating switchings and singular trajectories of the second order”, Math. Notes, 47:1 (1990), 41–49  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 1)

60. Soviet Math. Dokl., 39:1 (1989), 188–191  mathnet  mathscinet  isi

61. J. Appl. Math. Mech., 52:6 (1988), 731–737 (1990)  crossref  mathscinet  zmath  isi  scopus (cited: 1)
62. M. I. Zelikin, “Group symmetry in degenerate extremal problems”, Russian Math. Surveys, 43:2 (1988), 189–190  mathnet  crossref  mathscinet  zmath  adsnasa  isi
63. M. I. Zelikin, “Synthesis of optimal trajectories on representation spaces of Lie groups”, Math. USSR-Sb., 60:2 (1988), 533–546  mathnet  crossref  mathscinet  zmath

64. M. I. Zelikin, “The search for singular extremals”, Stochastic optimization (Kiev, 1984), Lecture Notes in Control and Inform. Sci., 81, Springer, Berlin, 1986, 738–746  crossref  mathscinet

65. M. I. Zelikin, “Minimization of integrals of differential forms, and degenerate variational problems”, Wiss. Z. Tech. Hochsch. Leuna-Merseburg, 27:5 (1985), 526–534  mathscinet  zmath
66. M. I. Zelikin, “On the singular arcs”, Problems Control Inform. Theory/Problemy Upravlen. Teor. Inform., 14:2 (1985), 75–88, R1–R15  mathscinet (cited: 1)  zmath  scopus (cited: 5)

67. M. I. Zelikin, “Necessary conditions for optimality of singular trajectories in problems that are linear with respect to control”, Some problems in modern analysis, Moskov. Gos. Univ. Mekh.-Mat. Fak., Moscow, 1984, 35–41  mathscinet  zmath
68. M. I. Zelikin, “Minimization of integrals of differential forms”, Dokl. Akad. Nauk SSSR, 278:5 (1984), 1057–1059  mathnet  mathscinet (cited: 1)  zmath  isi (cited: 1)
69. M. I. Zelikin, “On the theory of linear control problems”, Dokl. Akad. Nauk SSSR, 277:4 (1984), 782–785  mathnet (cited: 1)  mathscinet (cited: 1)  zmath  isi (cited: 3)

70. M. I. Zelikin, “Optimality conditions for singular trajectories in a problem of curvilinear integral minimization”, Dokl. Akad. Nauk SSSR, 267:3 (1982), 528–531  mathscinet  zmath  isi (cited: 2)

71. M. I. Zelikin, B. Ju. Sternin, “A system of integral equations that arises in the problem of S. L. Sobolev”, Sibirsk. Mat. Ž., 18:1 (1977), 97–102  mathscinet (cited: 3)  zmath

72. M. I. Zelikin, “A certain differential game with incomplete information”, Dokl. Akad. Nauk SSSR, 202 (1972), 998–1000  mathscinet (cited: 3)  zmath

73. M. I. Zelikin, N. T. Tynyanskii, “Determined differential games”, Uspekhi Mat. Nauk, 20:4(124) (1965), 151–157  mathnet  mathscinet  zmath


74. M. I. Zelikin, Control theory and optimization. I, Homogeneous spaces and the Riccati equation in the calculus of variations, Encyclopaedia of Mathematical Sciences, 86, Springer-Verlag, Berlin, 2000 , xii+284 pp.  mathscinet (cited: 17)  zmath

75. M. I. Zelikin, Odnorodnye prostranstva i uravnenie Rikkati v variatsionnom ischislenii, Faktorial, M., 1998 , 250 pp.  zmath

76. M. I. Zelikin, V. F. Borisov, Theory of chattering control, With applications to astronautics, robotics, economics, and engineering, Systems & Control: Foundations & Applications, Birkhäuser Boston Inc., Boston, MA, 1994 , xvi+242 pp.  mathscinet (cited: 72)  zmath

77. M. I. Zelikin, Optimalnoe upravlenie i variatsionnoe ischislenie, Izd-vo MGU, M., 1985 , 96 pp.  mathscinet (cited: 1)  zmath


78. M. I. Zelikin, “Chattering control in infinite-dimensional spaces”, Tezisy dokladov, Suzdal, 2009, 186


79. S. M. Aseev, V. M. Buchstaber, R. I. Grigorchuk, V. Z. Grines, B. M. Gurevich, A. A. Davydov, A. Yu. Zhirov, E. V. Zhuzhoma, M. I. Zelikin, A. B. Katok, A. V. Klimenko, V. V. Kozlov, V. P. Leksin, M. I. Monastyrskii, A. I. Neishtadt, S. P. Novikov, E. A. Sataev, Ya. G. Sinai, A. M. Stepin, “Dmitrii Viktorovich Anosov (obituary)”, Russian Math. Surveys, 70:2 (2015), 369–381  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
80. M. I. Zelikin, A. O. Ivanov, B. S. Kashin, A. S. Mishchenko, Yu. V. Nesterenko, A. A. Oshemkov, F. Yu. Popelenskii, V. A. Sadovnichii, A. A. Tuzhilin, V. N. Chubarikov, A. I. Shafarevich, A. N. Shiryaev, “Academician Anatolii Timofeevich Fomenko”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 6, 66–68  mathnet

81. M. I. Zelikin, “Lev Semenovich Pontryagin: reminiscences and reflections”, Istor.-Mat. Issled. (2), 2011, no. 14(49), 77–84, 357–358  mathscinet

82. Yu. S. Osipov, V. V. Kozlov, L. D. Faddeev, D. V. Anosov, V. S. Vladimirov, R. V. Gamkrelidze, A. A. Gonchar, N. N. Krasovskii, A. V. Kryazhimskii, A. B. Kurzhanskii, S. P. Novikov, S. M. Aseev, A. B. Zhizhchenko, D. V. Treschev, A. A. Agrachev, E. A. Volkov, N. L. Grigorenko, A. A. Davydov, M. I. Zelikin, A. Yu. Kolesov, A. A. Mal'tsev, M. S. Nikol'skii, N. Kh. Rozov, A. G. Sergeev, K. O. Besov, S. P. Konovalov, “In memory of Evgenii Frolovich Mishchenko”, Proc. Steklov Inst. Math., 271 (2010), 1–2  mathnet  crossref  mathscinet  isi

83. V. I. Arnol'd, L. R. Volevich, A. A. Gonchar, S. S. Demidov, M. I. Zelikin, Yu. S. Ilyashenko, G. G. Magaril-Il'yaev, A. V. Mikhalev, S. P. Novikov, I. V. Yaschenko, “Vladimir Mikhailovich Tikhomirov (on his 70th birthday)”, Russian Math. Surveys, 61:1 (2006), 189–192  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib

84. V. I. Arnol'd, A. S. Demidov, Yu. S. Ilyashenko, G. G. Magaril-Il'yaev, E. F. Mishchenko, K. Yu. Osipenko, A. B. Sossinski, M. A. Tsfasman, V. A. Uspenskii, M. N. Vyalyi, I. V. Yaschenko, M. I. Zelikin, “Vladimir M. Tikhomirov”, Mosc. Math. J., 5:1 (2005), 295  mathnet  mathscinet

85. A. A. Bolibrukh, A. A. Irmatov, M. I. Zelikin, O. B. Lupanov, V. M. Maynulov, E. F. Mishchenko, M. M. Postnikov, Yu. P. Solov'ev, E. V. Troitskii, “Aleksandr Sergeevich Mishchenko (on his 60th birthday)”, Russian Math. Surveys, 56:6 (2001), 1187–1191  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi

86. M. I. Zelikin, V. A. Il'in, N. N. Krasovskiĭ, et al., “Lyudmila Filippovna Zelikina”, Differential Equations, 35:6 (1999), 856–857  mathnet  mathscinet  isi

87. N. S. Bakhvalov, M. I. Zelikin, A. S. Kalashnikov, V. L. Kamynin, O. A. Oleinik, E. Yu. Panov, N. S. Petrosyan, V. M. Tikhomirov, A. V. Faminskii, V. N. Chubarikov, “Stanislav Nikolaevich Kruzhkov (obituary)”, Russian Math. Surveys, 53:5 (1998), 1071–1078  mathnet  crossref  crossref  mathscinet  zmath  isi

88. A. G. Vitushkin, M. I. Zelikin, N. N. Krasovskii, S. P. Novikov, Yu. S. Osipov, K. A. Sitnikov, “Nicolai Terent'evich Tynyanskii (obituary)”, Russian Math. Surveys, 41:4 (1986), 173–174  mathnet  crossref  mathscinet  adsnasa  isi

89. D. V. Anosov, V. I. Arnol'd, M. I. Zelikin, A. N. Kolmogorov, O. V. Lokutsievskii, Yu. S. Osipov, Ya. G. Sinai, V. M. Tikhomirov, M. V. Jakobson, “Vladimir Mikhailovich Alekseev (obituary)”, Russian Math. Surveys, 36:4 (1981), 201–206  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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