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

100%

Zweimüller R.

nr 2

295-302

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.

A joint limit theorem for compactly regenerative ergodic transformations

63%

Kocheim D. , Zweimüller R.

nr 1

33-45

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.