IJPAM: Volume 102, No. 1 (2015)

RYCHLIK'S THEOREM AND INVARIANT MEASURES FOR
RANDOM MAPS OF PIECEWISE EXPANDING $C^1$ MAPS
SATISFYING SUMMABLE OSCILLATION CONDITION

Shafiqul Islam
$^1$Department of Mathematics and Statistics
University of Prince Edward Island
550 University Ave, Charlottetown, PE, C1A 4P3, CANADA


Abstract. We prove a Rychlik's type theorem for random maps where each of the component maps is piecewise $C^1$, piecewise expanding and satisfies summabale oscillation condition.

We prove the existence of absolutely continuous invariant measures for random maps. Our results are generalizations of results of Góra, Li and Boyarsky in [7] of single piecewise expanding maps to results of random maps. We present an example for the stability of absolutely continuous invariant measures.

Received: January 14, 2015

AMS Subject Classification: 37A99

Key Words and Phrases: random maps, absolutely continuous invariant measure, harmonic average of slopes, summable oscillation condition, Rychlik's theorem

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DOI: 10.12732/ijpam.v102i1.10 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 102
Issue: 1
Pages: 105 - 116


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