Smoothness of invariant density for expanding transformations in higher dimensions. (2000) - Adl-Zarabi, Kourosh; Proppe, Harald
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 .