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.
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
ISTINA