Smoothness of invariant density for expanding transformations in higher dimensions

Kourosh Adl-Zarabi and Harald Proppe

International Journal of Stochastic Analysis, 2000, vol. 13, 1-8

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 .

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:180753

DOI: 10.1155/S1048953300000046

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