5 papers
Ergodic Theorems, Almost Invariant Sets, Value Distributions of Time Averagings
Valery V. Ryzhikov
It is shown how some deviations of ergodic averages can be structured. The deviations tend to zero almost everywhere. They are asymptotically almost invariant with respect to the a…
Singular geometric averages for ergodic multiflows
I. V. Bychkov, V. V. Ryzhikov
We consider ergodic multiflows on a probability space. The general theorem on universal averaging for multiflows is applied to averaging along manifolds in .
Explicit Infinite Mixing Automorphisms with Simple Spectra of Symmetric Squares
Sofia V. Vereshchagina, Valery V. Ryzhikov
We present mixing ergodic automorphisms of a space with sigma-finite measure whose symmetric tensor squares have simple spectra. This property is of interest in connection with dyn…
The full diapason of convergence rates of Birkhoff averages for ergodic flows
I. V. Podvigin, V. V. Ryzhikov
For an ergodic flow, a range of rates of convergence of Birkhoff averages from the maximum rate to an arbitrarily slow rate is realized by choosing the averaging function. For toru…
Generic extensions are recurrent for aperiodic probability automorphisms
D. K. Kozyreva, V. V. Ryzhikov
Generic extensions of aperiodic probability space automorphisms are recurrent.