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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Approximating the invariant densities of transformations with infinitely many pieces on the interval


Authors: P. Góra and A. Boyarsky
Journal: Proc. Amer. Math. Soc. 105 (1989), 922-928
MSC: Primary 58F11
MathSciNet review: 953006
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Abstract: Let $ I = [0,1]$ and $ \tau :I \to I$ be a piecewise continuous, expanding transformation with infinitely many pieces of monotonicity. We construct a sequence of transformations $ \left\{ {{\tau _n}} \right\}$, each having a finite partition, such that their invariant densities converge in $ {L_1}$ to the invariant density of $ \tau $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0953006-3
PII: S 0002-9939(1989)0953006-3
Article copyright: © Copyright 1989 American Mathematical Society