Smoothness of invariant density for expanding transformations in higher dimensions. (2000)

• Record Type: Journal Article
• Authors: Adl-Zarabi, Kourosh; Proppe, Harald
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 1(2000)
• Page Start: 33
• Page End: 40
• Publication Date: 2000
• Subjects: absolutely continuous invariant measure -- ergodic -- expanding transformation -- Perron-Frobenius operator; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953300000046
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : Let Ω be a bounded region in ℝ n and let 𝒫 = { P i } i = 1 m be a partition of Ω into a finite number of closed subsets having piecewise C 2 boundaries of finite ( n − 1 ) -dimensional measure. Let τ : Ω → Ω be an expanding transformation on 𝒫 where, τ i : τ | P i, and τ i ∈ C M, m ≥ 2 . We show that the τ -invariant density h ∈ C M − 2 .