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1
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Mixing on rank-one transformations

100%
Creutz D., Silva C.
Studia Mathematica
|
2010
|
tom 199
|
nr 1
43-72
EN
We prove that mixing on rank-one transformations is equivalent to "the uniform convergence of ergodic averages (as in the mean ergodic theorem) over subsequences of partial sums". In particular, all polynomial staircase transformations are mixing.
2
Content available remote

On v-positive type transformations in infinite measure

81%
Pădurariu T., Silva C., Zachos E.
Colloquium Mathematicum
|
2015
|
tom 140
|
nr 2
149-170
EN
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.
3
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On weakly mixing and doubly ergodic nonsingular actions

71%
Iams S., Katz B., Silva C., Street B., Wickelgren K.
Colloquium Mathematicum
|
2005
|
tom 103
|
nr 2
247-264
EN
We study weak mixing and double ergodicity for nonsingular actions of locally compact Polish abelian groups. We show that if T is a nonsingular action of G, then T is weakly mixing if and only if for all cocompact subgroups A of G the action of T restricted to A is weakly mixing. We show that a doubly ergodic nonsingular action is weakly mixing and construct an infinite measure-preserving flow that is weakly mixing but not doubly ergodic. We also construct an infinite measure-preserving flow whose cartesian square is ergodic.
4
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On μ-compatible metrics and measurable sensitivity

71%
Grigoriev I., Iordan M., Lubin A., Ince N., Silva C.
Colloquium Mathematicum
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2012
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tom 126
|
nr 1
53-72
EN
We introduce the notion of W-measurable sensitivity, which extends and strictly implies canonical measurable sensitivity, a measure-theoretic version of sensitive dependence on initial conditions. This notion also implies pairwise sensitivity with respect to a large class of metrics. We show that nonsingular ergodic and conservative dynamical systems on standard spaces must be either W-measurably sensitive, or isomorphic mod 0 to a minimal uniformly rigid isometry. In the finite measure-preserving case they are W-measurably sensitive or measurably isomorphic to an ergodic isometry on a compact metric space.
5
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Ergodicity and conservativity of products of infinite transformations and their inverses

62%
Clancy J., Friedberg R., Kasmalkar I., Loh I., Pădurariu T., Silva C., Vasudevan S.
Colloquium Mathematicum
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2016
|
tom 143
|
nr 2
271-291
EN
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 $T × T^{-1}$ 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.
6
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Ergodic properties of a class of discrete Abelian group extensions of rank-one transformations

62%
Dodd C., Jeasakul P., Jirapattanakul A., Kane D., Robinson B., Stein N., Silva C.
Colloquium Mathematicum
|
2010
|
tom 119
|
nr 1
1-22
EN
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.
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