The technique of studying of mixing properties of special flows is developed on the basis of properties of cocycle distribution. Original results about mixing properties of the measure preserving flows, including, flows on two-dimensional surfaces are received. A number of results about dependence of mixing properties of flows on the two-dimensional torus from smoothness and number of rotation is received also. Influence of fixed points on mixing properties of flows on surfaces is investigated. For ergodic with non atomic Borel measure flow on a compact manifold it is shown, that any time change is equivalent to differentiable one with the derivative continuous everywhere, except for one point.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1969, postgraduate study in 1972 (department of theory of functions and functional analysis). Ph.D. thesis was defended in 1974. At 80–90 ãã. I dealt with applied problems in engineering, a national economy, educational process. Dr.Sci. thesis was defended in 2005.
Main publications:
A. V. Kochergin, “Nondegenerate Saddles and Nonmixing Transformations II”, Math. Notes, 81:1 (2007), 126–129
A. V. Kochergin, “Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces”, Proc. Steklov Inst. Math., 256 (2007), 238–252
A. V. Kochergin, “Non-degenerate fixed points and mixing in flows on a 2-torus. II”, Sb. Math., 195:3 (2004), 317–346
A. V. Kočergin, “On mixing in special flows over a shifting of segments and in smooth flows on surfaces”, Math. USSR-Sb., 25:3 (1975), 441–469
A. V. Kočergin, “Time changes in flows and mixing”, Math. USSR-Izv., 7:6 (1973), 1273–1294
A. V. Kočergin, “On mixing in special flows over a shifting of segments and in smooth flows on surfaces”, Math. USSR-Sb., 25:3 (1975), 441–469
2.
A. V. Kočergin, “Nonsingular saddle points and the absence of mixing”, Math. Notes, 19:3 (1976), 277–286
3.
A. V. Kochergin, “Non-degenerate fixed points and mixing in flows on a 2-torus. II”, Sb. Math., 195:3 (2004), 317–346
4.
A. V. Kochergin, “Non-degenerate fixed points and mixing in flows on a 2-torus”, Sb. Math., 194:8 (2003), 1195–1224
5.
A. V. Kochergin, “A mixing special flow over a circle rotation with almost Lipschitz function”, Sb. Math., 193:3 (2002), 359–385
6.
A.V. Kočergin, “On the Absence of Mixing in special Flows over the Rotation of a Circle and in Flows on a Two-dimensional Torus.”, Soviet Mathematics - Doklady, 13:4 (1972), 949–952
7.
A. V. Kochergin, “Generalizations of theorems on mixing flows with non-degenerate saddle points on a 2-torus”, Sb. Math., 195:9 (2004), 1253–1270
8.
A. V. Kochergin, “Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces”, Proc. Steklov Inst. Math., 256 (2007), 238–252
9.
A. V. Kočergin, “Time changes in flows and mixing”, Math. USSR-Izv., 7:6 (1973), 1273–1294
10.
A. Kochergin, “Well approximable angles and mixing for flows on \bb T^2 with non-singular fixed points”, Electronic Research Announcements of the American Mathematical Society, 10:13 (2004), 113–121
A.V. Kočergin, “On the Homology of Functions over Dynamical Systems.”, Soviet Mathematics - Doklady, 17:6 (1976), 1637–1641
17.
A. V. Kochergin, “Hölder Time Change and Mixing Rate in a Flow on the Two-Dimensional Torus”, Proc. Steklov Inst. Math., 244 (2004), 201–232
18.
Kochergin A.V., “On discrete orbits for a cylindrical cascade with a Hölder function”, Mezhdunarodnaya konferentsiya «Sistemy Anosova i sovremennaya dinamika», posvyaschennaya 80-letiyu D.V.Anosova. Tezisy dokladov (Moskva, 19–23 dekabrya 2016 g.), MIAN, 2016, 60–62
19.
Kochergin A.V., “Uslovie Gëldera i diskretnye orbity tsilindricheskogo kaskada”, Mezhdunarodnaya konferentsiya po differentsialnym uravneniyam i dinamicheskim sistemam. Tezisy dokladov. (Suzdal, 8–12 iyulya 2016 g.), MIAN, Moskva, 2016, 107–108
20.
Andrey Kochergin, “A BESICOVITCH CYLINDRICAL TRANSFORMATION WITH HÖLDER FUNCTION”, Electronic Research Announcements in Mathematical Sciences, izdatelstvo American Mathematical Society, 22 (2015), 87–91 (Published online)
21.
A.V. Kochergin, “Nevyrozhdennye nepodvizhnye tochki v potokakh na poverkhnostyakh i otsutstvie peremeshivaniya.”, Differentsialnye uravneniya i topologiya: Mezhdunarodnaya kon-ferentsiya, posvyaschennaya 100-letiyu so dnya rozhdeniya L.S. Pontryagina: Tezisy dokladov (Moskva, 17–21 iyunya 2008.), Izd. otd. VMiK MGU im. M.V. Lomonosova; MAKS - Press, Moskva, 2008, 147
22.
Andrey Kochergin, “Causes of stretching of Birkhoff sums and mixing in flows on surfaces”, Dynamics, Ergodic Theory, and Geometry., Dedicated to Anatole Katok, Recent Progress in Dynamics. MSRI Publications, 54, Cambridge University Press, 2007, 129–144
23.
Kochergin Andrei Vasilevich, Primenenie teoretiko–funktsionalnykh i approksimatsionnykh metodov v issledovanii peremeshivayuschikh svoistv dinamicheskikh sistem, Avtoreferat diss. … dokt. fiz.-matem. nauk, MGU im. M.V. Lomonosova, mekh.-mat. fakultet, Moskva, 2005 , 24 pp.
24.
Kochergin Andrei Vasilevich, Primenenie teoretiko–funktsionalnykh i approksimatsionnykh metodov v issledovanii peremeshivayuschikh svoistv dinamicheskikh sistem, Diss. … dokt. fiz.-matem. nauk, MGU im. M.V. Lomonosova, mekh.-mat. fakultet, Moskva, 2004 , 244 pp.
25.
A.V. Kochergin, ““Diskretnye” effekty v gladkikh potokakh s nevyrozhdennymi sedlami na dvumernom tore.”, Mezhdunarodnaya konferentsiya “Differentsialnye uravneniya i smezhnye voprosy”, posvyaschennaya 103–letiyu so dnya rozhdeniya I.G. Petrovskogo. Sbornik tezisov. (Moskva, 16–22 maya 2004), Izdatelstvo Moskovskogo universiteta, Moskva, 2004, 107
26.
A.V. Kochergin, O svoistvakh peremeshivaniya u nekotorykh klassov potokov s invariantnoi meroi., Diss. … kand. fiz.-matem. nauk, Moskovskii gosudarstvennyi universitet im. M.V. Lomonosova, Moskva, 1974 , 113 pp.
27.
A.V. Kochergin, O svoistvakh peremeshivaniya u nekotorykh klassov potokov s invariantnoi meroi, Avtoreferat diss. … kand. fiz.-matem. nauk, Izdatelstvo Moskovskogo universiteta, Moskva, 1974 , 10 pp.
28.
V. M. Alekseev, A.V. Kočergin, V. M. El'jasberg, “On one method of approximation of processes in uniform biological structures.”, Automation and Remote Control, 34:8 (1973), 1244–1253
29.
A. V. Kochergin, “On the Growth of Birkhoff Sums over a Rotation of the Circle”, Math. Notes, 113:6 (2023), 784–793
30.
A. Yu. Zhirov, A. V. Kochergin, R. V. Plykin, E. A. Sataev, A. M. Stepin, “Dmitrii Viktorovich Anosov (on his 70th birthday)”, Russian Math. Surveys, 62:2 (2007), 401–402
31.
O. N. Ageev, Ya. B. Vorobets, B. Weiss, R. I. Grigorchuk, V. Z. Grines, B. M. Gurevich, L. S. Efremova, A. Yu. Zhirov, E. V. Zhuzhoma, B. S. Kashin, V. N. Kolokoltsov, A. V. Kochergin, L. M. Lerman, I. V. Mykytyuk, V. I. Oseledets, A. Yu. Plakhov, O. V. Pochinka, V. V. Ryzhikov, V. Zh. Sakbaev, A. G. Sergeev, Ya. G. Sinai, A. T. Tagi-Zade, S. V. Tikhonov, J.-P. Thouvenot, A. Ya. Helemskii, A. I. Shafarevich, “Anatolii Mikhailovich Stepin (obituary)”, Russian Math. Surveys, 77:2 (2022), 361–367
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