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Absolutely continuous invariant measures for most piecewise smooth expanding maps

Published online by Cambridge University Press:  06 August 2002

WILLIAM J. COWIESON
WILLIAM J. COWIESON
Affiliation:
Department of Mathematics, Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012-1185, USA
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Abstract

We introduce transversality conditions for a piecewise smooth map in any dimension with a sufficiently regular discontinuity set. We prove that maps satisfying these conditions have certain nice properties and, among all maps with a common set of discontinuities, form an open and dense subset. This, in conjunction with other works of the author, implies the existence of stochastically stable invariant densities for an open and dense set of piecewise smooth expanding maps.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 4 , August 2002 , pp. 1061 - 1078
Copyright
© 2002 Cambridge University Press

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