# American Institute of Mathematical Sciences

2000, 6(2): 451-458. doi: 10.3934/dcds.2000.6.451

## Absolutely continuous invariant measures for piecewise $C^2$ and expanding mappings in higher dimensions

 1 Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406-5045, United States 2 Institute of Systems Science, Academia Sinica, Beijing 100080, China

Received  June 1999 Revised  November 1999 Published  January 2000

In this paper, by using a trace theorem in the theory of functions of bounded variation, we prove the existence of absolutely continuous invariant measures for a class of piecewise expanding mappings of general bounded domains in any dimension.
Citation: Jiu Ding, Aihui Zhou. Absolutely continuous invariant measures for piecewise $C^2$ and expanding mappings in higher dimensions. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 451-458. doi: 10.3934/dcds.2000.6.451
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