Mixing on rank-one transformations

Darren Creutz; Cesar E. Silva

The search session has expired. Please query the service again.

Displaying similar documents to “Mixing on rank-one transformations”

Ergodic seminorms for commuting transformations and applications

Bernard Host (2009)

Studia Mathematica

Similarity:

Recently, T. Tao gave a finitary proof of a convergence theorem for multiple averages with several commuting transformations, and soon thereafter T. Austin gave an ergodic proof of the same result. Although we give here another proof of the same theorem, this is not the main goal of this paper. Our main concern is to provide tools for the case of several commuting transformations, similar to the tools successfully used in the case of a single transformation, with the idea that they may...

Convergence of multiple ergodic averages along cubes for several commuting transformations

Qing Chu (2010)

Studia Mathematica

Similarity:

We prove the norm convergence of multiple ergodic averages along cubes for several commuting transformations, and derive corresponding combinatorial results. The method we use relies primarily on the "magic extension" established recently by B. Host.

Tower multiplexing and slow weak mixing

Terrence Adams (2015)

Colloquium Mathematicae

Similarity:

A technique is presented for multiplexing two ergodic measure preserving transformations together to derive a third limiting transformation. This technique is used to settle a question regarding rigidity sequences of weak mixing transformations. Namely, given any rigidity sequence for an ergodic measure preserving transformation, there exists a weak mixing transformation which is rigid along the same sequence. This establishes a wide range of rigidity sequences for weakly mixing dynamical...

Power weakly mixing infinite transformations.

Day, Sarah L., Grivna, Brian R., McCartney, Earle P., Silva, Cesar E. (1999)

The New York Journal of Mathematics [electronic only]

Similarity:

Some thoughts about Segal's ergodic theorem

Daniel W. Stroock (2010)

Colloquium Mathematicae

Similarity:

Over fifty years ago, Irving Segal proved a theorem which leads to a characterization of those orthogonal transformations on a Hilbert space which induce ergodic transformations. Because Segal did not present his result in a way which made it readily accessible to specialists in ergodic theory, it was difficult for them to appreciate what he had done. The purpose of this note is to state and prove Segal's result in a way which, I hope, will win it the recognition which it deserves. ...

Weak mixing of a transformation similar to Pascal

Daniel M. Kane (2007)

Colloquium Mathematicae

Similarity:

We construct a class of transformations similar to the Pascal transformation, except for the use of spacers, and show that these transformations are weakly mixing.

Power weak mixing does not imply multiple recurrence in infinite measure and other counterexamples.

Gruher, Kate, Hines, Fred, Patel, Deepam, Silva, Cesar E., Waelder, Robert (2003)

The New York Journal of Mathematics [electronic only]

Similarity:

On the Pointwise Ergodic Behaviour of Transformations Preserving Infinite Measures

Jon Aaronson (1977)

Publications mathématiques et informatique de Rennes

Similarity:

Conjugacies between ergodic transformations and their inverses

Geoffrey Goodson (2000)

Colloquium Mathematicae

Similarity:

We study certain symmetries that arise when automorphisms S and T defined on a Lebesgue probability space (X, ℱ, μ) satisfy the equation $S T = T^{- 1} S$ . In an earlier paper [6] it was shown that this puts certain constraints on the spectrum of T. Here we show that it also forces constraints on the spectrum of $S^{2}$ . In particular, $S^{2}$ has to have a multiplicity function which only takes even values on the orthogonal complement of the subspace $f \in L^{2} (X, ℱ, μ) : f (T^{2} x) = f (x)$ . For S and T ergodic satisfying this equation further constraints...

Constructions of cocycles over irrational rotations

W. Bułatek, M. Lemańczyk, D. Rudolph (1997)

Studia Mathematica

Similarity:

We construct a coboundary cocycle which is of bounded variation, is homotopic to the identity and is Hölder continuous with an arbitrary Hölder exponent smaller than 1.

A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. III. Relative isomorphism of non-ergodic transformations

Štefan Šujan (1985)

Kybernetika

Similarity:

Abelian Cocycles for Nonsingular Ergodic Transformations and the Genericity of Type III... Transformations.

J.R. Choksi, J.M. Hawkins (1987)

Monatshefte für Mathematik

Similarity:

Dynamics of finite-multivalued transformations.

Igudesman, Konstantin B. (2005)

Lobachevskii Journal of Mathematics

Similarity:

On a pointwise ergodic theorem for multiparameter semigroups.

Ryotaro Sato (1994)

Publicacions Matemàtiques

Similarity:

Let T_i (i = 1, 2, ..., d) be commuting null preserving transformations on a finite measure space (X, F, μ) and let 1 ≤ p < ∞. In this paper we prove that for every f ∈ L_p(μ) the averages A_nf(x) = (n + 1)^-d Σ_{0≤n_i≤n} f(T₁ ^n₁T₂ ^n_2...

Ergodic properties of a class of discrete Abelian group extensions of rank-one transformations

Chris Dodd, Phakawa Jeasakul, Anne Jirapattanakul, Daniel M. Kane, Becky Robinson, Noah D. Stein, Cesar E. Silva (2010)

Colloquium Mathematicae

Similarity:

We define a class of discrete Abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply recurrent. We then study conditions sufficient for showing that Cartesian products of transformations are conservative for a class of invertible infinite measure-preserving transformations and provide examples of these transformations.

Ergodicity and conservativity of products of infinite transformations and their inverses

Julien Clancy, Rina Friedberg, Indraneel Kasmalkar, Isaac Loh, Tudor Pădurariu, Cesar E. Silva, Sahana Vasudevan (2016)

Colloquium Mathematicae

Similarity:

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation T in the class, the cartesian product T × T is ergodic, but the product $T \times T^{- 1}$ is not. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.