Displaying similar documents to “Central limit theorems for non-invertible measure preserving maps”

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.

Waiting for long excursions and close visits to neutral fixed points of null-recurrent ergodic maps

Roland Zweimüller (2008)

Fundamenta Mathematicae

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We determine, for certain ergodic infinite measure preserving transformations T, the asymptotic behaviour of the distribution of the waiting time for an excursion (from some fixed reference set of finite measure) of length larger than l as l → ∞, generalizing a renewal-theoretic result of Lamperti. This abstract distributional limit theorem applies to certain weakly expanding interval maps, where it clarifies the distributional behaviour of hitting times of shrinking neighbourhoods of...

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.

On a pointwise ergodic theorem for multiparameter semigroups.

Ryotaro Sato (1994)

Publicacions Matemàtiques

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Let Ti (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 ∈ Lp(μ) the averages Anf(x) = (n + 1)-d Σ0≤ni≤n f(T1 n1 T2 n2...

Completely mixing maps without limit measure

Gerhard Keller (2004)

Colloquium Mathematicae

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We combine some results from the literature to give examples of completely mixing interval maps without limit measure.

Ergodic properties of skew products with Lasota-Yorke type maps in the base

Zbigniew Kowalski (1993)

Studia Mathematica

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We consider skew products T ( x , y ) = ( f ( x ) , T e ( x ) y ) preserving a measure which is absolutely continuous with respect to the product measure. Here f is a 1-sided Markov shift with a finite set of states or a Lasota-Yorke type transformation and T i , i = 1,..., max e, are nonsingular transformations of some probability space. We obtain the description of the set of eigenfunctions of the Frobenius-Perron operator for T and consequently we get the conditions ensuring the ergodicity, weak mixing and exactness of T....