Topological groups with Rokhlin properties

Eli Glasner; Benjamin Weiss

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Displaying similar documents to “Topological groups with Rokhlin properties”

Tower multiplexing and slow weak mixing

Terrence Adams (2015)

Colloquium Mathematicae

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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...

A mixing dynamical system on the Cantor set.

Kim, Jeong H. (1995)

International Journal of Mathematics and Mathematical Sciences

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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]

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Weak mixing of a transformation similar to Pascal

Daniel M. Kane (2007)

Colloquium Mathematicae

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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.

On ergodic transformations that are both weakly mixing and uniformly rigid.

James, Jennifer, Koberda, Thomas, Lindsey, Kathryn, Silva, Cesar E., Speh, Peter (2009)

The New York Journal of Mathematics [electronic only]

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Multiple Rokhlin tower theorem: A simple proof.

Eigen, S.J., Prasad, V.S. (1997)

The New York Journal of Mathematics [electronic only]

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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]

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Groups of Measure Preserving Transformations.

H. Rindler (1987/88)

Mathematische Annalen

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On a pointwise ergodic theorem for multiparameter semigroups.

Ryotaro Sato (1994)

Publicacions Matemàtiques

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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...

Characterizing mildly mixing actions by orbit equivalence of products.

Hawkins, Jane, Silva Cesar, E. (1998)

The New York Journal of Mathematics [electronic only]

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Generic points in the cartesian powers of the Morse dynamical system

Emmanuel Lesigne, Anthony Quas, Máté Wierdl (2003)

Bulletin de la Société Mathématique de France

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The symbolic dynamical system associated with the Morse sequence is strictly ergodic. We describe some topological and metrical properties of the Cartesian powers of this system, and some of its other self-joinings. Among other things, we show that non generic points appear in the fourth power of the system, but not in lower powers. We exhibit various examples and counterexamples related to the property of weak disjointness of measure preserving dynamical systems.

Infinite ergodic index $ℤ^{d}$ -actions in infinite measure

E. Muehlegger, A. Raich, C. Silva, M. Touloumtzis, B. Narasimhan, W. Zhao (1999)

Colloquium Mathematicae

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We construct infinite measure preserving and nonsingular rank one $ℤ^{d}$ -actions. The first example is ergodic infinite measure preserving but with nonergodic, infinite conservative index, basis transformations; in this case we exhibit sets of increasing finite and infinite measure which are properly exhaustive and weakly wandering. The next examples are staircase rank one infinite measure preserving $ℤ^{d}$ -actions; for these we show that the individual basis transformations have conservative...

A joint limit theorem for compactly regenerative ergodic transformations

David Kocheim, Roland Zweimüller (2011)

Studia Mathematica

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We study conservative ergodic infinite measure preserving transformations satisfying a compact regeneration property introduced by the second-named author in J. Anal. Math. 103 (2007). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector (Zₙ,Sₙ), where Zₙ and Sₙ are respectively the time of the last visit before time n to, and the occupation time of, a suitable set Y of finite measure.

Weakly mixing transformations and the Carathéodory definition of measurable sets

Amos Koeller, Rodney Nillsen, Graham Williams (2007)

Colloquium Mathematicae

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Let 𝕋 denote the set of complex numbers of modulus 1. Let v ∈ 𝕋, v not a root of unity, and let T: 𝕋 → 𝕋 be the transformation on 𝕋 given by T(z) = vz. It is known that the problem of calculating the outer measure of a T-invariant set leads to a condition which formally has a close resemblance to Carathéodory's definition of a measurable set. In ergodic theory terms, T is not weakly mixing. Now there is an example, due to Kakutani, of a transformation ψ̃ which is weakly mixing but...

An analog of the Marcinkiewicz integral in ergodic theory

Roger Jones (1980)

Studia Mathematica

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On v-positive type transformations in infinite measure

Tudor Pădurariu, Cesar E. Silva, Evangelie Zachos (2015)

Colloquium Mathematicae

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For each vector v we define the notion of a v-positive type for infinite-measure-preserving transformations, a refinement of positive type as introduced by Hajian and Kakutani. We prove that a positive type transformation need not be (1,2)-positive type. We study this notion in the context of Markov shifts and multiple recurrence, and give several examples.

Absolutely continuous, invariant measures for dissipative, ergodic transformations

Jon Aaronson, Tom Meyerovitch (2008)

Colloquium Mathematicae

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We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.