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. Kochergin, “On the Growth of Birkhoff Sums over a Rotation of the Circle”, Math. Notes, 113:6 (2023), 784–793
2022
2.
A. B. Antonevich, A. V. Kochergin, A. A. Shukur, “Behaviour of Birkhoff sums generated by rotations of the circle”, Sb. Math., 213:7 (2022), 891–924
3.
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
2020
4.
Kochergin Andrey, “Besicovitch cascades and bounded partial quotients”, Applied Mathematics and Nonlinear Sciences, 5:2 (2020), 267–278 (Published online)
A. V. Kochergin, “New examples of Besicovitch transitive cylindrical cascades”, Sb. Math., 209:9 (2018), 1257–1272
2016
6.
A. V. Kochergin, “Besicovitch Cylindrical Transformation with a Hölder Function”, Math. Notes, 99:3 (2016), 382–389
7.
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
8.
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
2015
9.
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)
2008
10.
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
2007
11.
A. V. Kochergin, “Nondegenerate Saddles and Nonmixing Transformations II”, Math. Notes, 81:1 (2007), 126–129
12.
A. V. Kochergin, “Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces”, Proc. Steklov Inst. Math., 256 (2007), 238–252
13.
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
14.
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
2005
15.
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.
2004
16.
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
17.
A. V. Kochergin, “Non-degenerate fixed points and mixing in flows on a 2-torus. II”, Sb. Math., 195:3 (2004), 317–346
18.
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
19.
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
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.
21.
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
2003
22.
A. V. Kochergin, “Non-degenerate fixed points and mixing in flows on a 2-torus”, Sb. Math., 194:8 (2003), 1195–1224
2002
23.
A. V. Kochergin, “A mixing special flow over a circle rotation with almost Lipschitz function”, Sb. Math., 193:3 (2002), 359–385
1976
24.
A. V. Kočergin, “Nonsingular saddle points and the absence of mixing”, Math. Notes, 19:3 (1976), 277–286
25.
A.V. Kočergin, “On the Homology of Functions over Dynamical Systems.”, Soviet Mathematics - Doklady, 17:6 (1976), 1637–1641
1975
26.
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
1974
27.
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.
28.
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.
1973
29.
A. V. Kočergin, “Time changes in flows and mixing”, Math. USSR-Izv., 7:6 (1973), 1273–1294
30.
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
1972
31.
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
2023
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