01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
15.09.1961
E-mail:
,
Keywords:
averaging,
fast and slow motions,
large deviations,
entropy,
equilibrium states,
weighted shift operator,
Legendre transform.
Subject:
averaging principle in systems with fast and slow motions,
large deviations in stochastic processes,
hyperbolic dynamical systems,
thermodynamic formalism and variational principles in dynamical systems.
Biography
EDUCATION:
1978–1983 Moscow State University,
department of mechanics and mathematics;
1983–1986 Moscow State University,
Post-graduate course at the chair of differential equations;
1996–1999 Belarusian State University, Minsk, Doctoral studies.
DEGREES:
Ph.D. 1987, Moscow State University, Moscow, USSR, title of the thesis:
"On the averaging method in multifrequency systems";
Doctor of Science degree 2002, Steklov Institute of Mathematics, Moscow, Russia, title of the thesis: "Cramer asymptotics
in systems with slow and intermixing fast motions".
Main publications:
Bakhtin V. I., “Averaging in multifrequency systems”, Funct. Anal. Appl., 20 (1986), 83–88
Bakhtin V. I., “Cramér asymptotics in a system with slow and fast Markovian motions”, Theory Probab. Appl., 44:1 (1999), 1–17
Bakhtin V. I., Kifer Yu., “Diffusion approximation for slow motion in fully coupled averaging”, Probability theory and related fields, 129 (2004), 157–181
Bakhtin V. I., “Positive processes”, Ergodic theory and dynamical systems, 27 (2007), 639–670
Antonevich A. B., Bakhtin V. I., Lebedev A. V., “On $t$-entropy and variational principle for the spectral radius of transfer and weighted shift operators”, Ergodic theory and dynamical systems, 31 (2011), 995–1042
V. I. Bakhtin, B. Sadok, “Packing dimensions of basins generated by distributions on a finite alphabet”, Journal of the Belarusian State University. Mathematics and Informatics, 2 (2021), 6–16
V. I. Bakhtin, “Spectral potential, Kullback action, and large deviations of empirical measures on measurable spaces”, Teor. Veroyatnost. i Primenen., 59:4 (2014), 625–638; Theory Probab. Appl., 59:4 (2015), 535–544
V. I. Bakhtin, “Estimators for an exponential family of distributions based on indirect observations”, Tr. Inst. Mat., 21:2 (2013), 54–62
2012
6.
V. I. Bakhtin, “Riesz Theorem for Positive Multilinear Functions”, Mat. Zametki, 92:4 (2012), 628–631; Math. Notes, 92:4 (2012), 570–573
7.
V. I. Bakhtin, “An approach to the Lebesgue integral by means of outer integral norm”, Tr. Inst. Mat., 20:1 (2012), 22–32
2011
8.
A. B. Antonevich, V. I. Bakhtin, A. V. Lebedev, “Crossed product of a $C^*$-algebra by an endomorphism, coefficient algebras and transfer operators”, Mat. Sb., 202:9 (2011), 3–34; Sb. Math., 202:9 (2011), 1253–1283
V. I. Bakhtin, “A conditional extremum necessary condition in terms of local algebras”, Tr. Inst. Mat., 19:2 (2011), 3–6
2009
10.
V. I. Bakhtin, V. V. Gorokhovik, “Optimality conditions of first and second order in vector optimization problems on metric spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 15:4 (2009), 32–43; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S28–S39
V. I. Bakhtin, “Cramér Asymptotics in the Averaging Method for Systems with Fast Hyperbolic Motions”, Trudy Mat. Inst. Steklova, 244 (2004), 65–86; Proc. Steklov Inst. Math., 244 (2004), 58–79
V. I. Bakhtin, “Foliated Functions and an Averaged Weighted Shift Operator for Perturbations of Hyperbolic Mappings”, Trudy Mat. Inst. Steklova, 244 (2004), 35–64; Proc. Steklov Inst. Math., 244 (2004), 29–57
V. I. Bakhtin, “Cramér asymptotics in a system with slow and fast Markovian motions”, Teor. Veroyatnost. i Primenen., 44:1 (1999), 14–33; Theory Probab. Appl., 44:1 (2000), 1–17
V. I. Bakhtin, “Large deviations of random variables with a finite number of approximately evaluated cumulants”, Teor. Veroyatnost. i Primenen., 42:3 (1997), 603–608; Theory Probab. Appl., 42:3 (1998), 513–517
V. I. Bakhtin, “A direct method of constructing an invariant measure on a hyperbolic attractor”, Izv. RAN. Ser. Mat., 56:5 (1992), 934–957; Russian Acad. Sci. Izv. Math., 41:2 (1993), 207–227
V. I. Bakhtin, “Averaging in a single-frequency system in general position”, Differ. Uravn., 27:9 (1991), 1493–1505; Differ. Equ., 27:9 (1991), 1051–1061
V. I. Bakhtin, “Weierstrass–Malgrange preparation theorem in the finitely smooth case”, Funktsional. Anal. i Prilozhen., 24:2 (1990), 3–15; Funct. Anal. Appl., 24:1 (1990), 86–96
V. I. Bakhtin, “On the transversality of mappings, pre-images of mappings, and the representation of sets of degenerate matrices as images”, Uspekhi Mat. Nauk, 42:2(254) (1987), 217–218; Russian Math. Surveys, 42:2 (1987), 271–272
23.
V. I. Bakhtin, “The topological normal forms of metamorphoses of caustics of the series $\mathbf{D}_\mu$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1987, no. 4, 58–61
24.
V. I. Bakhtin, “A strengthened extremal property of Chebyshev polynomials”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1987, no. 2, 45–46
1986
25.
V. I. Bakhtin, “Averaging in multifrequency systems”, Funktsional. Anal. i Prilozhen., 20:2 (1986), 1–7; Funct. Anal. Appl., 20:2 (1986), 83–88
V. I. Bakhtin, “Properties of the entropy and Hausdorff dimensions”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1982, no. 5, 25–29
1985
28.
V. Ya. Rivkind, S. P. Novikov, V. M. Petkov, V. P. Myasnikov, M. V. Fedoryuk, V. V. Kucherenko, A. A. Davydov, A. I. Neishtadt, S. N. Kruzhkov, S. A. Molchanov, A. A. Ruzmaikin, D. D. Sokolov, Yu. M. Sukhov, A. G. Shukhov, B. R. Vainberg, V. I. Bakhtin, A. G. Vainshtein, B. Z. Shapiro, V. A. Kondrat'ev, O. A. Oleinik, M. I. Vishik, S. B. Kuksin, A. G. Korolev, Yu. S. Ilyashenko, “Sessions of the Petrovskii seminar on differential equations and mathemathical problems of physics”, Uspekhi Mat. Nauk, 40:5(245) (1985), 295–307
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