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Displaying similar documents to “Waiting for long excursions and close visits to neutral fixed points of null-recurrent ergodic 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.

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...

Ergodic properties of skew products withfibre maps of Lasota-Yorke type

Zbigniew Kowalski (1994)

Applicationes Mathematicae

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We consider the skew product transformation T(x,y)= (f(x), T e ( x ) ) where f is an endomorphism of a Lebesgue space (X,A,p), e : X → S and T s s ∈ S is a family of Lasota-Yorke type maps of the unit interval into itself. We obtain conditions under which the ergodic properties of f imply the same properties for T. Consequently, we get the asymptotical stability of random perturbations of a single Lasota-Yorke type map. We apply this to some probabilistic model of the motion of cogged bits in the rotary...

S-unimodal Misiurewicz maps with flat critical points

Roland Zweimüller (2004)

Fundamenta Mathematicae

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We consider S-unimodal Misiurewicz maps T with a flat critical point c and show that they exhibit ergodic properties analogous to those of interval maps with indifferent fixed (or periodic) points. Specifically, there is a conservative ergodic absolutely continuous σ-finite invariant measure μ, exact up to finite rotations, and in the infinite measure case the system is pointwise dual ergodic with many uniform and Darling-Kac sets. Determining the order of return distributions to suitable...

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...

Ergodic theory approach to chaos: Remarks and computational aspects

Paweł J. Mitkowski, Wojciech Mitkowski (2012)

International Journal of Applied Mathematics and Computer Science

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We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor...

Central limit theorems for non-invertible measure preserving maps

Michael C. Mackey, Marta Tyran-Kamińska (2008)

Colloquium Mathematicae

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Using the Perron-Frobenius operator we establish a new functional central limit theorem for non-invertible measure preserving maps that are not necessarily ergodic. We apply the result to asymptotically periodic transformations and give a specific example using the tent map.