Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 1, Pages 33-40
Smoothness of invariant density for expanding transformations in higher dimensions
1Dawson College, Department of Mathematics, 3040 Sherbrooke St. West, Montreal H3Z 1A4, Canada
2Concordia University, Department of Mathematics and Statistics, 7141 Sherbrooke St. West, Montreal H4B 1R6, Canada
Received 1 August 1998; Revised 1 September 1999
Copyright © 2000 Kourosh Adl-Zarabi and Harald Proppe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a bounded region in and let be a partition of
into a finite number of closed subsets having piecewise boundaries of
finite -dimensional measure. Let be an expanding transformation on where, , and , . We show that the
-invariant density .