Wyniki wyszukiwania

1

Hopf's ratio ergodic theorem by inducing

100%

Zweimüller R.

Colloquium Mathematicum

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2004

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tom 101

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nr 2

289-292

EN

We present a very quick and easy proof of the classical Stepanov-Hopf ratio ergodic theorem, deriving it from Birkhoff's ergodic theorem by a simple inducing argument.

2

Poisson suspensions of compactly regenerative transformations

100%

Zweimüller R.

Colloquium Mathematicum

|

2008

|

tom 110

|

nr 1

211-225

EN

For infinite measure preserving transformations with a compact regeneration property we establish a central limit theorem for visits to good sets of finite measure by points from Poissonian ensembles. This extends classical results about (noninteracting) infinite particle systems driven by Markov chains to the realm of systems driven by weakly dependent processes generated by certain measure preserving transformations.

3

S-unimodal Misiurewicz maps with flat critical points

100%

Zweimüller R.

Fundamenta Mathematicae

|

2004

|

tom 181

|

nr 1

1-25

EN

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 reference sets we obtain bounds on the decay of correlations and on wandering rates. Assuming some control of the local behaviour of T at c, we show that in most cases, e.g. whenever the postcritical orbit has a Lyapunov exponent, the tail of the return distribution is in fact regularly varying, which implies various distributional limit theorems.

4

Exact $𝓒^{∞}$ covering maps of the circle without (weak) limit measure

100%

Zweimüller R.

Colloquium Mathematicum

|

2002

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tom 93

|

nr 2

295-302

EN

We construct $𝓒^{∞}$ maps T on the interval and on the circle which are Lebesgue exact preserving an absolutely continuous infinite measure μ ≪ λ, such that for any probability measure ν ≪ λ the sequence $(n^{-1} ∑_{k=0}^{n-1} ν∘T^{-k})_{n≥1}$ of arithmetical averages of image measures does not converge weakly.

5

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

100%

Zweimüller R.

Fundamenta Mathematicae

|

2008

|

tom 198

|

nr 2

125-138

EN

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 neutral fixed points.

6

A joint limit theorem for compactly regenerative ergodic transformations

64%

Kocheim D., Zweimüller R.

Studia Mathematica

|

2011

|

tom 203

|

nr 1

33-45

EN

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.

Ograniczanie wyników

3 Colloquium Mathematicum

2 Fundamenta Mathematicae

1 Studia Mathematica

6 Zweimüller R.

1 Kocheim D.

1 2011

2 2008

2 2004

1 2002

Hopf's ratio ergodic theorem by inducing

Poisson suspensions of compactly regenerative transformations

S-unimodal Misiurewicz maps with flat critical points

Exact $𝓒^{∞}$ covering maps of the circle without (weak) limit measure

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