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pro vyhledávání: '"Ryzhikov, Valery"'
Autor:
Ryzhikov, Valery V.
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 recall shortly some results and discuss related problems.
Externí odkaz:
http://arxiv.org/abs/2411.07234
Autor:
Ryzhikov, Valery V.
For every natural $n>1$, there is an operator $T$ of dynamical origin such that its tensor power $T^{\otimes n}$ has singular spectrum, and $T^{\otimes (n+1)}$ has absolutely continuous one. For a set $D$ of positive measure there are mixing zero ent
Externí odkaz:
http://arxiv.org/abs/2411.02024
Autor:
Ryzhikov, Valery V.
We answer the question of Frantzikinakis and Host about the convergence of ergodic $(n^2,n^3)$-averages and consider a more general case. Let sequences ${ p(n)},{ q(n)}$ satisfy the property $ p(n+1)- p(n), \ q(n+1)- q(n)\ \to\ +\infty.$ Then there e
Externí odkaz:
http://arxiv.org/abs/2410.11787
Autor:
Ryzhikov, Valery V.
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 infinite mixing automorphisms also are rank-one.
Externí odkaz:
http://arxiv.org/abs/2407.21768
Autor:
Ryzhikov, Valery V.
Content of the lectures is the following. Properties of transformations equivalent to ergodicity. Birkhoff's Theorem. Properties equivalent to weak mixing. On typical properties of transformations. Lego to construct transformations. Typical entropy i
Externí odkaz:
http://arxiv.org/abs/2407.20180
Autor:
Ryzhikov, Valery V.
Typical properties of measure space automorphisms with respect to the Halmos and Alpern-Tikhonov metrics are discussed.
Externí odkaz:
http://arxiv.org/abs/2407.18236
Autor:
Ryzhikov, Valery V.
In connection with the results of Tim Austin, and Wen Huang, Song Shao, Xiangdong Ye we present the following assertion: there are infinite automorphisms $S,T$, some set $A$ of positive finite measure and a sequence $N_m$ with $|N_{m+1}|/|N_m|\ \to\i
Externí odkaz:
http://arxiv.org/abs/2407.13741
Autor:
Ryzhikov, Valery V.
Let $T$ be a staircase rank-one construction with parameters $r_j \sim j^d$, $0
Externí odkaz:
http://arxiv.org/abs/2407.02140
Autor:
Ryzhikov, Valery V.
Let $T$ be a staircase rank-one construction with parameters $r_j \sim j^d$, $0
Externí odkaz:
http://arxiv.org/abs/2407.01514
Autor:
Ryzhikov, Valery V.
Simple Sidon automorphisms are asymmetric. Poisson suspensions over them are mixing and asymmetric.
Comment: includes English and Russian versions
Comment: includes English and Russian versions
Externí odkaz:
http://arxiv.org/abs/2406.14390