Ergodic theory; mathematical physics; statistical physics; random processes.
Main publications:
Markovskie tsepi, kosye proizvedeniya i ergodicheskie teoremy dlya obschikh dinamicheskikh sistem // Teoriya veroyatnostei i ee prilozheniya, 1965, 10, 551–557.
O spektre ergodicheskikh avtomorfizmov // DAN SSSR, 1966, 168, 1009–1011.
Kolmogorovskaya teoriya turbulentnosti i evolyutsiya sostoyanii sistem kletochnykh avtomatov tipa reshetochnogo gaza. Invariantnye sostoyaniya // Teoriya veroyatnostei i ee prilozheniya, 1989, 34,165–177.
Fast dynamo problem for a smooth map on a two-torus // Geophys. and Astrophys. Fluid Dynamics, 1993, 73, 133–145.
Z. I. Bezhaeva, V. I. Oseledets, “Quantum Markov states and quantum hidden Markov states”, Zap. Nauchn. Sem. POMI, 468 (2018), 13–23; J. Math. Sci. (N. Y.), 240:5 (2019), 507–514
2017
2.
Z. I. Bezhaeva, V. L. Kulikov, E. F. Olekhova, V. I. Oseledets, “Erdős measures on the Euclidean space and on the group of $A$-adic integers”, Tr. Mat. Inst. Steklova, 297 (2017), 38–45; Proc. Steklov Inst. Math., 297 (2017), 28–34
2015
3.
Z. I. Bezhaeva, V. I. Oseledets, “Remarks on Quantum Markov States”, Funktsional. Anal. i Prilozhen., 49:3 (2015), 60–65; Funct. Anal. Appl., 49:3 (2015), 205–209
2012
4.
Z. I. Bezhaeva, V. I. Oseledets, “Calculation of the entropy for a hidden Markov chain”, Diskr. Mat., 24:1 (2012), 108–122; Discrete Math. Appl., 22:2 (2012), 207–223
5.
Z. I. Bezhaeva, V. I. Oseledets, “The entropy of the Erdos measure for the pseudogolden ratio”, Teor. Veroyatnost. i Primenen., 57:1 (2012), 158–167; Theory Probab. Appl., 57:1 (2013), 135–144
2010
6.
Z. I. Bezhaeva, V. I. Oseledets, “The Erdős–Vershik problem for the golden ratio”, Funktsional. Anal. i Prilozhen., 44:2 (2010), 3–13; Funct. Anal. Appl., 44:2 (2010), 83–91
2006
7.
Z. I. Bezhaeva, V. I. Oseledets, “Erdős measures for the goldenshift and Markov chains of the second order”, Teor. Veroyatnost. i Primenen., 51:1 (2006), 5–21; Theory Probab. Appl., 51:1 (2007), 28–41
2005
8.
Z. I. Bezhaeva, V. I. Oseledets, “Erdős measures, sofic measures, and Markov chains”, Zap. Nauchn. Sem. POMI, 326 (2005), 28–47; J. Math. Sci. (N. Y.), 140:3 (2007), 357–368
2001
9.
V. I. Oseledets, D. V. Khmelev, “Stochastic Transportation Networks and Stability of Dynamical Systems”, Teor. Veroyatnost. i Primenen., 46:1 (2001), 147–154; Theory Probab. Appl., 46:1 (2002), 154–161
2000
10.
V. I. Oseledets, D. V. Khmelev, “Global Stability of Infinite Systems of Nonlinear Differential Equations and Nonhomogeneous Countable Markov Chains”, Probl. Peredachi Inf., 36:1 (2000), 60–76; Problems Inform. Transmission, 36:1 (2000), 54–70
1997
11.
Z. I. Bezhaeva, V. I. Oseledets, “Concerning a stochastic dynamical system”, Mat. Zametki, 61:6 (1997), 803–809; Math. Notes, 61:6 (1997), 675–680
12.
N. D. Cong, V. I. Oseledets, “Topological invariants of linear cocycles of an ergodic map”, Tr. Mat. Inst. Steklova, 216 (1997), 243–256; Proc. Steklov Inst. Math., 216 (1997), 236–249
1996
13.
Z. I. Bezhaeva, V. I. Oseledets, “An Example of a Strange Nonchaotic Attractor”, Funktsional. Anal. i Prilozhen., 30:4 (1996), 1–9; Funct. Anal. Appl., 30:4 (1996), 223–229
14.
Z. I. Bezhaeva, V. I. Oseledets, “On the symmetric $\sigma$-algebra of a stationary Harris Markov process”, Teor. Veroyatnost. i Primenen., 41:4 (1996), 869–877; Theory Probab. Appl., 41:4 (1997), 741–748
15.
Z. I. Bezhaeva, V. I. Oseledets, “On the variance of sums for functions of a stationary Markov process”, Teor. Veroyatnost. i Primenen., 41:3 (1996), 633–639; Theory Probab. Appl., 41:3 (1997), 537–541
1989
16.
V. I. Oseledets, “On a new way of writing the Navier–Stokes equation.
The Hamiltonian formalism”, Uspekhi Mat. Nauk, 44:3(267) (1989), 169–170; Russian Math. Surveys, 44:3 (1989), 210–211
17.
V. I. Oseledetz, “Kolmogorov's Theory of Turbulence and Evolution of the Lattice-Gas-Type System of Cell Automates. Invariant States”, Teor. Veroyatnost. i Primenen., 34:1 (1989), 165–177; Theory Probab. Appl., 34:1 (1989), 140–152
1983
18.
V. I. Oseledets, “Completely positive linear mappings, non-Hamiltonian evolution, and quantum stochastic processes”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 20 (1983), 52–94; J. Soviet Math., 25:6 (1984), 1529–1557
1977
19.
B. M. Gurevich, V. I. Oseledets, “Some mathematical problems related to the nonequilibrium statistical mechanics of infinitely many particles”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 14 (1977), 5–39; J. Soviet Math., 13:4 (1980), 455–478
1973
20.
B. M. Gurevich, V. I. Oseledets, “Gibbs distributions and dissipativeness of $U$-diffeomorphisms”, Dokl. Akad. Nauk SSSR, 209:5 (1973), 1021–1023
1971
21.
V. I. Oseledets, “Two nonisomorphic dynamical systems with the same simple continuous spectrum”, Funktsional. Anal. i Prilozhen., 5:3 (1971), 75–79; Funct. Anal. Appl., 5:3 (1971), 233–236
1969
22.
V. I. Oseledets, “An automorphism with simple, continuous spectrum not having the group property”, Mat. Zametki, 5:3 (1969), 323–326; Math. Notes, 5:3 (1969), 196–198
1968
23.
V. I. Oseledets, “A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems”, Tr. Mosk. Mat. Obs., 19 (1968), 179–210; Trans. Moscow Math. Soc., 19 (1968), 197–231
1966
24.
V. I. Oseledets, “The spectrum of ergodic automorphisms”, Dokl. Akad. Nauk SSSR, 168:5 (1966), 1009–1011
1965
25.
V. I. Oseledets, “Markov chains, skew products and ergodic theorems for “general” dynamic systems”, Teor. Veroyatnost. i Primenen., 10:3 (1965), 551–557; Theory Probab. Appl., 10:3 (1965), 499–504
1996
26.
S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 51:4(310) (1996), 179–191; Russian Math. Surveys, 51:4 (1996), 765–778
27.
B. M. Gurevich, I. A. Ibragimov, R. A. Minlos, I. A. Ovseevich, V. I. Oseledets, M. S. Pinsker, V. V. Prelov, Yu. V. Prokhorov, Ya. G. Sinai, A. S. Holevo, A. N. Shiryaev, “Roland L'vovich Dobrushin (20 July 1919 – 12 November 1995)”, Teor. Veroyatnost. i Primenen., 41:1 (1996), 164–169; Theory Probab. Appl., 41:1 (1997), 132–136