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, “New examples of Besicovitch transitive cylindrical cascades”, Sb. Math., 209:9 (2018), 1257–1272
5.
A. V. Kochergin, “Besicovitch Cylindrical Transformation with a Hölder Function”, Math. Notes, 99:3 (2016), 382–389
6.
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)
7.
A. V. Kochergin, “Nondegenerate Saddles and Nonmixing Transformations II”, Math. Notes, 81:1 (2007), 126–129
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.
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
10.
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
11.
A. V. Kochergin, “Non-degenerate fixed points and mixing in flows on a 2-torus. II”, Sb. Math., 195:3 (2004), 317–346
12.
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
13.
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. Kochergin, “Non-degenerate fixed points and mixing in flows on a 2-torus”, Sb. Math., 194:8 (2003), 1195–1224
15.
A. V. Kochergin, “A mixing special flow over a circle rotation with almost Lipschitz function”, Sb. Math., 193:3 (2002), 359–385
16.
A. V. Kočergin, “Nonsingular saddle points and the absence of mixing”, Math. Notes, 19:3 (1976), 277–286
17.
A.V. Kočergin, “On the Homology of Functions over Dynamical Systems.”, Soviet Mathematics - Doklady, 17:6 (1976), 1637–1641
18.
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
19.
A. V. Kočergin, “Time changes in flows and mixing”, Math. USSR-Izv., 7:6 (1973), 1273–1294
20.
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
21.
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
Thesis
22.
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.
23.
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.
24.
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.
25.
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.
Proceedings
26.
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
27.
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
28.
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
29.
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
Personalia
30.
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
31.
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
Contact us: