01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
4.12.1954
E-mail:
Keywords:
differential equations,
linear systems,
linear equations,
Hamiltonian systems,
stability,
Lyapunov's exponents,
oscillation,
wondering,
Baire's classification,
control system.
UDC:
517.926
Subject:
Ordinary differential equations, linear differential systems and equations, Hamiltonian systems, qualitative theory of differential equations, stability theory, theory of Lyapunov exponents, oscillation theory, Baire's discontinuous functions theory, control systems theory.
Main publications:
I. N. Sergeev, “K teorii pokazatelei Lyapunova lineinykh sistem differentsialnykh uravnenii”, Trudy seminara im. I. G. Petrovskogo, 9, 1983, 111–166
I. N. Sergeev, “Formula dlya vychisleniya minimalnogo pokazatelya trekhmernoi sistemy”, Differents. uravneniya, 36:3 (2000), 345–354
I. N. Sergeev, “Opredelenie i svoistva kharakteristicheskikh chastot lineinogo uravneniya”, Trudy seminara im. I. G. Petrovskogo, 25, 2006, 249–294
I. N. Sergeev, “Ob upravlenii resheniyami lineinogo differentsialnogo uravneniya”, Vestnik Mosk. un-ta. Ser. 1. Matem., mekh., 2009, № 3, 25–33
I. N. Sergeev, “Kharakteristiki koleblemosti i bluzhdaemosti reshenii lineinoi differentsialnoi sistemy”, Izv. RAN. Ser. matem., 76:1 (2012), 149–172
I. N. Sergeev, “Study of the Complete Oscillation, Rotation, and Wandering Properties of a Differential System by the First Approximation”, Mat. Zametki, 115:4 (2024), 610–618; Math. Notes, 115:4 (2024), 599–606
2.
I. N. Sergeev, “Examples of autonomous differential systems with contrast combination of measures of Lyapunov, Perron, and upper-limit stability”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, no. 1, 50–54; Moscow University Mathematics Bulletin, 79:1 (2024), 55–59
3.
I. N. Sergeev, “Dependence on the initial moment of the measure of stability and instability of the zero solution
to a differential system”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 34:1 (2024), 80–90
2023
4.
I. N. Sergeev, “Definition and Properties of Measures of Stability and Instability of Zero Solution of a Differential System”, Mat. Zametki, 113:6 (2023), 895–904; Math. Notes, 113:6 (2023), 831–839
I. N. Sergeev, “О перроновских, ляпуновских и верхнепредельных свойствах устойчивости дифференциальных систем”, Tr. Semim. im. I. G. Petrovskogo, 33 (2023), 353–423
I. N. Sergeev, “Classes of linear approximations providing various types of stability or instability of differential systems”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 4, 8–15; Moscow University Mathematics Bulletin, 78:4 (2023), 163–169
7.
I. N. Sergeev, K. V. Umansky, “Criterion of Lyapunov reducibility of a linear autonomous differential system to a linear autonomous equation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 1, 55–59; Moscow University Mathematics Bulletin, 78:1 (2023), 52–56
2022
8.
A.A. Bondarev, I. N. Sergeev, “Examples of differential systems with contrasting combinations of Lyapunov, Perron, and upper-limit properties”, Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022), 25–29; Dokl. Math., 106:2 (2022), 322–325
I. N. Sergeev, “The definition of the indices of oscillation, rotation, and wandering of nonlinear differential systems”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 3, 41–46; Moscow University Mathematics Bulletin, 76:3 (2021), 129–134
I. N. Sergeev, “Plane rotability exponents of a linear system of differential equations”, Tr. Semim. im. I. G. Petrovskogo, 32 (2019), 325–348; J. Math. Sci. (N. Y.), 244:2 (2020), 320–334
I. N. Sergeev, “Reducibility of linear differential systems to linear differential equations”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, no. 3, 39–44; Moscow University Mathematics Bulletin, 74:3 (2019), 121–126
I. N. Sergeev, “Oscillation, rotatability, and wandering characteristic indicators for differential systems determining rotations of plane”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, no. 1, 21–26; Moscow University Mathematics Bulletin, 74:1 (2019), 20–24
I. N. Sergeev, “On simplified formulas for the central exponents of differential systems with non-uniform scales”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 10, 60–78; Russian Math. (Iz. VUZ), 62:10 (2018), 51–67
I. N. Sergeev, “Oscillation, rotation, and wandering of solutions to linear differential systems”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132 (2017), 117–121; J. Math. Sci. (N. Y.), 230:5 (2018), 770–774
I. N. Sergeev, “Oscillation, Rotation, and Wandering Exponents of Solutions of Differential Systems”, Mat. Zametki, 99:5 (2016), 732–751; Math. Notes, 99:5 (2016), 729–746
I. N. Sergeev, “Lyapunov characteristics of oscillation, rotation, and wandering of solutions of differential systems”, Tr. Semim. im. I. G. Petrovskogo, 31 (2016), 177–219; J. Math. Sci. (N. Y.), 234:4 (2018), 497–522
I. N. Sergeev, “The complete set of relations between the oscillation, rotation and wandering indicators of solutions of differential systems”, Izv. IMI UdGU, 2015, no. 2(46), 171–183
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, N. A. Izobov, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, V. V. Palin, N. Kh. Rozov, M. S. Romanov, I. N. Sergeev, E. V. Radkevich, O. S. Rozanova, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Scientific heritage of Vladimir Mikhailovich Millionshchikov”, Tr. Semim. im. I. G. Petrovskogo, 30 (2014), 5–41; J. Math. Sci. (N. Y.), 210:2 (2015), 115–134
2013
20.
I. N. Sergeev, “The remarkable agreement between the oscillation and wandering characteristics of solutions of differential systems”, Mat. Sb., 204:1 (2013), 119–138; Sb. Math., 204:1 (2013), 114–132
I. N. Sergeev, “Properties of characteristic frequencies of linear equations of arbitrary order”, Tr. Semim. im. I. G. Petrovskogo, 29 (2013), 414–442; J. Math. Sci. (N. Y.), 197:3 (2014), 410–426
I. N. Sergeev, “Oscillation and wandering characteristics of solutions of a linear differential system”, Izv. RAN. Ser. Mat., 76:1 (2012), 149–172; Izv. Math., 76:1 (2012), 139–162
I. N. Sergeev, “Oscillation and wandering of solutions to a second order differential equation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 6, 21–26
I. N. Sergeev, “Definition and properties of characteristic frequencies of a linear equation”, Tr. Semim. im. I. G. Petrovskogo, 25 (2006), 249–294; J. Math. Sci. (N. Y.), 135:1 (2006), 2764–2793
I. N. Sergeev, “A formula for the minimal exponent of a three-dimensional system”, Differ. Uravn., 36:3 (2000), 345–354; Differ. Equ., 36:3 (2000), 388–398
27.
I. N. Sergeev, “An upper estimate for the minimal exponent of a three-dimensional system”, Differ. Uravn., 36:1 (2000), 114–123; Differ. Equ., 36:1 (2000), 132–142
28.
I. N. Sergeev, “On the attainability of minimal exponents in the class of infinitesimal perturbations”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2000, no. 3, 61–63
I. N. Sergeev, “The rotation method and singular numbers of three-dimensional systems”, Differ. Uravn., 35:12 (1999), 1630–1639; Differ. Equ., 35:12 (1999), 1655–1664
30.
I. N. Sergeev, “A lower bound for the minimal exponent of a three-dimensional system”, Differ. Uravn., 35:10 (1999), 1387–1397; Differ. Equ., 35:10 (1999), 1407–1417
31.
I. N. Sergeev, “A formula for the minorant of one of the Lyapunov exponents”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1999, no. 4, 22–29
1991
32.
I. N. Sergeev, “On minimal exponents of a triangular system and of the system of its diagonal approximation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1991, no. 6, 42–44
1987
33.
G. V. Osinnikova, I. N. Sergeev, “The unattainability of central indices in a class of regular systems”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1987, no. 4, 39–44
1986
34.
O. I. Morozov, I. N. Sergeev, “Destabilizability of linear Hamiltonian systems”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1986, no. 4, 38–41
1980
35.
I. N. Sergeev, “Invariance of central exponents with respect to perturbations which approach zero at infinity”, Differ. Uravn., 16:9 (1980), 1719
36.
I. N. Sergeev, “The interior of a set of systems of differential equations with a stable Ljapunov exponent”, Differ. Uravn., 16:6 (1980), 1135–1137
37.
I. N. Sergeev, “Sharp upper bounds of mobility of the Ljapunov exponents of a system of differential equations and the behavior of the exponents under perturbations approaching”, Differ. Uravn., 16:3 (1980), 438–448
I. N. Sergeev, “The existence of a solution with small growth for biregular differential systems with random perturbation”, Differ. Uravn., 13:11 (1977), 2088–2092
2023
39.
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Goritsky, N. V. Denisova, Yu. S. Ilyashenko, T. O. Kapustina, A. A. Kon'kov, V. V. Palin, E. V. Radkevich, V. V. Rogachev, O. S. Rozanova, M. S. Romanov, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, M. V. Shamolin, T. A. Shaposhnikova, “К 70-летию Валерия Васильевича Козлова”, Tr. Semim. im. I. G. Petrovskogo, 33 (2023), 3–7
2022
40.
V. V. Aleksandrov, S. B. Gashkov, D. V. Georgievskii, O. S. Dudakova, V. P. Karlikov, B. S. Kashin, G. M. Kobel'kov, M. D. Kovalev, V. V. Kozlov, R. M. Kolpakov, V. V. Kochergin, T. P. Lukashenko, A. S. Mishchenko, Yu. V. Nesterenko, R. I. Nigmatulin, N. P. Red'kin, V. A. Sadovnichii, I. N. Sergeev, A. T. Fomenko, A. V. Chashkin, V. N. Chubarikov, A. I. Shafarevich, A. N. Shiryaev, V. Ya. Shkadov, A. A. Shkalikov, “90 years since the birthday of Academician Oleg Borisovich Lupanov (02.06.1932 – 03.05.2006)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2022, no. 3, 3–5
2021
41.
V. V. Aleksandrov, S. B. Gashkov, D. V. Georgievskii, V. P. Karlikov, B. S. Kashin, G. M. Kobel'kov, V. V. Kozlov, T. P. Lukashenko, A. S. Mishchenko, Yu. V. Nesterenko, R. I. Nigmatulin, O. V. Popov, V. A. Sadovnichii, I. N. Sergeev, G. V. Fedorov, A. T. Fomenko, A. I. Shafarevich, A. N. Shiryaev, V. Ya. Shkadov, A. A. Shkalikov, “To 70-th anniversary of professor V. N. Chubarikov”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 5, 69–71
2019
42.
Yu. A. Alkhutov, V. F. Butuzov, V. V. Kozlov, A. A. Kon'kov, A. V. Mikhalev, E. I. Moiseev, E. V. Radkevich, N. Kh. Rozov, V. A. Sadovnichii, I. N. Sergeev, M. D. Surnachev, R. N. Tikhomirov, V. N. Chubarikov, T. A. Shaposhnikova, A. A. Shkalikov, “Vasilii Vasilievich Zhikov”, Tr. Semim. im. I. G. Petrovskogo, 32 (2019), 5–7; J. Math. Sci. (N. Y.), 244:2 (2020), 113–115
2018
43.
B. A. Budak, D. V. Goryashin, A. S. Zelenskii, A. I. Kozko, V. S. Panferov, A. G. Razborov, I. N. Sergeev, I. A. Sheipak, “Олимпиада «Ломоносов»-2018. Математика”, Kvant, 2018, no. 11, 54–55
44.
A. I. Aptekarev, O. P. Vinogradov, V. N. Dubrovsky, M. Koloskova, T. P. Lukashenko, I. I. Mel'nikov, Yu. V. Nesterenko, M. K. Potapov, I. Yu. Selivanova, K. V. Semenov, I. N. Sergeev, A. P. Solodov, A. I. Strogova, V. N. Chubarikov, E. V. Shivrinskaya, “Valerii Vasil'evich Vavilov (30.06.1946 – 21.10.2016)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, no. 1, 71–72
2017
45.
D. V. Goryashin, A. S. Zelenskii, A. I. Kozko, L. V. Kritskov, V. S. Panferov, A. G. Razborov, I. N. Sergeev, I. A. Sheipak, M. V. Yumashev, “Олимпиада «Покори Воробьевы горы!»”, Kvant, 2017, no. 9, 53–55
46.
D. V. Goryashin, A. S. Zelenskii, A. I. Kozko, L. V. Kritskov, V. S. Panferov, A. G. Razborov, I. N. Sergeev, I. A. Sheipak, M. V. Yumashev, S. S. Chesnokov, “Олимпиада «Ломоносов»-2017”, Kvant, 2017, no. 4, 52–58
2014
47.
I. V. Gaishun, A. A. Gryzlov, V. Ya. Derr, N. A. Izobov, A. I. Karpov, E. K. Makarov, G. V. Merzlyakova, N. N. Petrov, S. N. Popova, L. I. Rodina, N. Kh. Rozov, I. N. Sergeev, A. A. Tolstonogov, V. N. Ushakov, A. G. Chentsov, “In memory of Evgenii Leonidovich Tonkov (27.06.1940–28.09.2014)”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4, 146–154
2011
48.
M. S. Agranovich, I. V. Astashova, L. A. Bagirov, V. V. Vlasov, V. V. Zhikov, Yu. S. Ilyashenko, V. V. Kozlov, A. A. Kon'kov, S. I. Pokhozhaev, E. V. Radkevich, N. Kh. Rozov, I. N. Sergeev, A. L. Skubachevskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010”, CMFD, 39 (2011), 5–10; Journal of Mathematical Sciences, 190:1 (2013), 1–7
49.
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. Yu. Goritskii, N. V. Denisova, V. V. Zhikov, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, M. S. Romanov, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Olga Arsenjevna Oleinik”, Tr. Semim. im. I. G. Petrovskogo, 28 (2011), 5–7; J. Math. Sci. (N. Y.), 179:3 (2011), 345–346
2010
50.
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, V. V. Kozlov, V. A. Kondratiev, A. A. Kon'kov, N. Kh. Rozov, I. N. Sergeev, V. N. Chubarikov, A. T. Fomenko, A. S. Shamaev, “To memory of Vladimir Mikhailovich Millionshchikov”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2010, no. 2, 71–72
2008
51.
A. Begunts, S. Voloshin, V. Voronin, E. Grigor'ev, D. Denisov, A. Zoteev, V. Korolev, T. Lukashenko, G. Medvedev, V. Panferov, V. Pogozhev, A. Razgulin, I. Sergeev, A. Sklyankin, V. Ushakov, E. Khailov, S. Chesnokov, E. Shikin, B. Shchedrin, “Московский государственный университет им. М.В. Ломоносова”, Kvant, 2008, no. 1, 45–53
2007
52.
S. Avvakumov, A. Begunts, P. Borodin, S. Voloshin, V. Voronin, N. Grigorenko, E. Grigor'ev, D. Denisov, A. Zoteev, Yu. Kiselev, S. Kozlov, I. Lomov, G. Medvedev, A. Nevzorov, V. Panferov, V. Pogozhev, A. Razgulin, S. Samsonov, I. Sergeev, A. Sklyankin, V. Ushakov, E. Khailov, S. Chesnokov, E. Shikin, A. Shcheglov, B. Shchedrin, “Московский государственный университет им. М.В. Ломоносова”, Kvant, 2007, no. 1, 44–52
53.
I. V. Astashova, L. A. Bagirov, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, G. V. Grishina, N. V. Denisova, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, V. M. Millionshchikov, V. A. Nikishkin, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, V. A. Sadovnichii, V. S. Samovol, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, A. F. Filippov, T. S. Khachlaev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev on the 70th anniversary of his birth”, Tr. Semim. im. I. G. Petrovskogo, 26 (2007), 5–28; J. Math. Sci. (N. Y.), 143:4 (2007), 3183–3197
2006
54.
S. Avvakumov, V. Bening, S. Voloshin, V. Voronin, E. Grigor'ev, D. Denisov, A. Zoteev, N. Levshin, I. Lomov, G. Medvedev, V. Panferov, V. Pogozhev, A. Razgulin, I. Sergeev, A. Sklyankin, V. Ushakov, E. Khailov, S. Chesnokov, E. Shikin, A. Shcheglov, B. Shchedrin, “Московский государственный университет им. М.В. Ломоносова”, Kvant, 2006, no. 1, 44–52
2005
55.
V. Bening, P. Borodin, V. Voronin, E. Grigor'ev, D. Denisov, A. V. Zoteev, I. Inovenkov, N. Levshin, I. Lomov, G. Medvedev, A. Pavlikov, V. S. Panferov, V. Pogozhev, M. Potapov, A. Razgulin, I. Sergeev, A. Sklyankin, V. Ushakov, M. Fedotov, E. Khailov, S. Chesnokov, O. Shalygina, B. Shchedrin, “Московский государственный университет им. М.В. Ломоносова”, Kvant, 2005, no. 1, 40–49
56.
I. V. Astashova, L. A. Bagirov, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, G. V. Grishina, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, O. B. Lupanov, I. V. Matrosov, V. M. Millionshchikov, V. A. Nikishkin, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, V. A. Sadovnichii, V. S. Samovol, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, A. F. Filippov, T. S. Khachlaev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, A. A. Shkalikov, “Vladimir Aleksandrovich Kondrat'ev”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2005, no. 5, 77–79
I. A. Vinogradova, O. B. Lupanov, I. I. Mel'nikov, M. K. Potapov, V. A. Sadovnichii, I. N. Sergeev, “In memory of Slav Nickolaevich Olekhnik”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, no. 4, 108–109
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