16 citations · 51 across the 58 of their papers we have counts for
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Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals
Valery V. Ryzhikov
We recall theorems by Krygin, Atkinson, Shneiberg and propose the following assertion. Let be an ergodic flow on , let a function on have zero mean, and $μ(A)>…
Multiple mixing, 75 years of Rokhlin's problem
Valery V. Ryzhikov
In 1949, V.A. Rokhlin introduced new invariants for measure-preserving transformations, called k-fold mixing. Does mixing imply k-fold mixing? -- this problem remains open. We reca…
Spectra and joint dynamics of Poisson suspensions for rank-one automorphisms
Valery V. Ryzhikov
For every natural , there is an operator of dynamical origin such that its tensor power has singular spectrum, and has absolutely conti…
Non-recurrence and divergent -averages for deterministic automorphisms
Valery V. Ryzhikov
We answer the question of Frantzikinakis and Host about the convergence of ergodic -averages and consider a more general case. Let sequences satisfy th…
Non-commuting transformations with non-converging 2-fold ergodic averages
Valery V. Ryzhikov
In connection with the results of Tim Austin, and Wen Huang, Song Shao, Xiangdong Ye we present the following assertion: there are infinite automorphisms , some set of pos…
Typical infinite mixing automorphisms are rank-one
Valery V. Ryzhikov
Bashtanov proved that generic mixing automorphisms of probability space with respect to the Alpern-Tikhonov metric had rank one. Using Sidon's constructions, we show that generic i…