Adl-Zarabi, Kourosh; Proppe, Harald Smoothness of invariant density for expanding transformations in higher dimensions. (English) Zbl 0954.37011 J. Appl. Math. Stochastic Anal. 13, No. 1, 33-40 (2000). For an expanding map \(T:\Omega\to\Omega\) with the property that the region \(\Omega\subset{\mathbb R}^d\) has a partition into finitely many closed regions, each with piecewise \(C^2\) boundaries of finite \((n-1)\)-dimensional volume, and on each partition \(T\) restricts to a \(C^k\) map, \(k\geq 2\), it is shown here that the absolutely continuous \(T\)-invariant measure on \(\Omega\) has density in \(C^{k-2}\). Reviewer: Thomas Ward (Norwich) MSC: 37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems Keywords:absolutely continuous invariant measure; Perron-Frobenius operator PDFBibTeX XMLCite \textit{K. Adl-Zarabi} and \textit{H. Proppe}, J. Appl. Math. Stochastic Anal. 13, No. 1, 33--40 (2000; Zbl 0954.37011) Full Text: DOI EuDML