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

Jiu Ding; Aihui Zhou

doi:10.3934/dcds.2000.6.451

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2000, Volume 6, Issue 2: 451-458. Doi: 10.3934/dcds.2000.6.451

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

Jiu Ding^1, and
Aihui Zhou^2,

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

Received: June 1999

Revised: November 1999

Published: April 2000

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Abstract

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.

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Mathematics Subject Classification: 58F11, 58F15.

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