- Tytuł:
- Distortion inequality for the Frobenius-Perron operator and some of its consequences in ergodic theory of Markov maps in $ℝ^d$
- Autorzy:
- Bugiel, Piotr
- Powiązania:
- https://bibliotekanauki.pl/articles/1294475.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
invariant measure
Frobenius-Perron operator
expanding map
distortion inequality - Opis:
- Asymptotic properties of the sequences (a) ${P^j_φ g}_{j=1}^{∞}$ and (b) ${j^{-1} ∑_{i=0}^{j-1} Pⁱ_φ g}_{j=1}^{∞}$, where $P_φ:L¹ → L¹$ 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 $ℝ^d$. Also the Bernoulli property is proved for a class of smooth Markov maps in $ℝ^d$.
- Źródło:
-
Annales Polonici Mathematici; 1998, 68, 2; 125-157
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł