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Currently displaying 1 – 5 of 5

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Invariant Measures of C...-Diffeomorphisms of Markov Type in R...

Piotr Bugiel — 1992

Monatshefte für Mathematik

Approximation for the invariant measures of Markov maps in Rd.

Piotr Bugiel — 1996

Mathematische Zeitschrift

On a Bernoulli Property of some Piecewise C2-Diffeomorphisms in ...d.

Piotr Bugiel — 1993

Monatshefte für Mathematik

On the convergence of the iterates of the Frobenius-Perron operator associated with a Markov map defined on an interval. The lower-function approach

Piotr Bugiel — 1991

Annales Polonici Mathematici

Distortion inequality for the Frobenius-Perron operator and some of its consequences in ergodic theory of Markov maps in $ℝ^{d}$

Piotr Bugiel — 1998

Annales Polonici Mathematici

Asymptotic properties of the sequences (a) ${P_{φ}^{j} g}_{j = 1}^{\infty}$ and (b) ${j^{- 1} \sum_{i = 0}^{j - 1} P ⁱ_{φ} g}_{j = 1}^{\infty}$ , where $P_{φ} : L ¹ \to L ¹$ is the Frobenius-Perron operator associated with a nonsingular Markov map defined on a σ-finite measure space, are studied for g ∈ G = f ∈ L¹: f ≥ 0 and ⃦f ⃦ = 1. An operator-theoretic analogue of Rényi’s Condition is introduced. It is proved that under some additional assumptions this condition implies the L¹-convergence of the sequences (a) and (b) to a unique g₀ ∈ G. The general result is applied to some smooth Markov maps in $ℝ^{d}$ ....

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