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Invariant measures and the compactness of the domain

Marian Jabłoński, Paweł Góra (1998)

Annales Polonici Mathematici

We consider piecewise monotonic and expanding transformations τ of a real interval (not necessarily bounded) into itself with countable number of points of discontinuity of τ’ and with some conditions on the variation V [ 0 , x ] ( 1 / | τ ' | ) which need not be a bounded function (although it is bounded on any compact interval). We prove that such transformations have absolutely continuous invariant measures. This result generalizes all previous “bounded variation” existence theorems.

Inverse limit of M -cocycles and applications

Jan Kwiatkowski (1998)

Fundamenta Mathematicae

For any m, 2 ≤ m < ∞, we construct an ergodic dynamical system having spectral multiplicity m and infinite rank. Given r > 1, 0 < b < 1 such that rb > 1 we construct a dynamical system (X, B, μ, T) with simple spectrum such that r(T) = r, F*(T) = b, and C ( T ) / w c l T n : n ∈ ℤ = ∞

Large deviations for generic stationary processes

Emmanuel Lesigne, Dalibor Volný (2000)

Colloquium Mathematicae

Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.

Currently displaying 241 – 260 of 601