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



   2018
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

   2017
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

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

   2013
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)

   2012
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

   2011
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

   2010
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

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

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

   2009
20. 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)
21. 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

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

   2008
23. 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
24. 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)

   2004
25. 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
26. M. I. Zelikin, “Optimal problems on Hölder function spaces”, J. Math. Sci. (N. Y.), 121:2 (2004), 2265–2280  mathnet  crossref  mathscinet  zmath

   2006
27. 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)

   2004
28. 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
29. J. Appl. Math. Mech., 68:4 (2004), 617–622  crossref  mathscinet  zmath  isi  scopus  scopus
30. 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)

   2005
31. 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)

   2003
32. M. I. Zelikin, “Hölderian extremal problems”, Patterns and waves (Saint Petersburg, 2002), AkademPrint, St. Petersburg, 2003, 412–432  mathscinet
33. 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
34. M. I. Zelikin, V. F. Borisov, “Optimal chattering feedback control”, J. Math. Sci. (N. Y.), 114:3 (2003), 1227–1344  mathnet  crossref  mathscinet  zmath

   2002
35. M. I. Zelikin, “Chattering on optimal trajectories of Hölder problems”, Sb. Math., 193:5 (2002), 669–683  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
36. 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

   2001
37. Differ. Equ., 37:9 (2001), 1217–1223  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
38. M. I. Zelikin, “Optimal control in Hölder classes of functions”, Dokl. Akad. Nauk, 378:6 (2001), 733–736  mathnet  mathscinet  zmath
39. 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
40. 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
41. M. I. Zelikin, “Synthesis of Optimal Trajectories That Defines the Reeb Foliation”, Proc. Steklov Inst. Math., 233 (2001), 81–86  mathnet  mathscinet  zmath

   2000
42. 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
43. 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
44. 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

   1999
45. Differential Equations, 35:11 (1999), 1489–1493 (2000)  mathnet  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
46. 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
47. M. I. Zelikin, L. F. Zelikina, “Exact Constants in Kolmogorov-Type Inequalities”, Proc. Steklov Inst. Math., 227 (1999), 131–139  mathnet  mathscinet  zmath
48. M. I. Zelikin, “Optimal Synthesis Containing Successively Inserted Chattering Bundles”, Proc. Steklov Inst. Math., 224 (1999), 137–148  mathnet  mathscinet  zmath

   1998
49. 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
50. 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
51. M. I. Zelikin, Odnorodnye prostranstva i uravnenie Rikkati v variatsionnom ischislenii, Faktorial, M., 1998 , 250 pp.  zmath
52. 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)

   1997
53. 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
54. 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

   1996
55. 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)

   1995
56. 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
57. M. I. Zelikin, “Irregularity of optimal control in regular extremal problems”, Fundam. Prikl. Mat., 1:2 (1995), 399–408  mathnet  mathscinet  zmath

   1994
58. 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
59. 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

   1993
60. 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

   1991
61. 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)

   1992
62. 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)

   1990
63. 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)

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

   1988
65. J. Appl. Math. Mech., 52:6 (1988), 731–737 (1990)  crossref  mathscinet  zmath  isi  scopus (cited: 1)
66. M. I. Zelikin, “Group symmetry in degenerate extremal problems”, Russian Math. Surveys, 43:2 (1988), 189–190  mathnet  crossref  mathscinet  zmath  adsnasa  isi
67. 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

   1986
68. 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

   1985
69. M. I. Zelikin, Optimalnoe upravlenie i variatsionnoe ischislenie, Izd-vo MGU, M., 1985 , 96 pp.  mathscinet (cited: 1)  zmath
70. 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
71. 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)

   1984
72. 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
73. 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)
74. 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)

   1982
75. 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)

   1977
76. 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

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

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