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2008, Volume 22, Issue 3: 529-540. Doi: 10.3934/dcds.2008.22.529
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Deterministic representation for position dependent random maps

  • 1.

    Economics, University of Manchester, Oxford Road, Manchester, M13 9PL

  • 2.

    Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria, BC, Canada V8W 3P4

  • 3.

    Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, B.C., V8W 3R4

Received:  June 30, 2007
Revised:  January 31, 2008
Published:  August 2008
Abstract Related Papers Cited by
    Abstract
  • We give a deterministic representation for position dependent random maps and describe the structure of its set of invariant measures. Our construction generalizes the skew product representation of random maps with constant probabilities. In particular, we establish one-to-one correspondence between eigenfunctions corresponding to eigenvalues of unit modulus for the Frobenius-Perron (transfer) operator of the random map and for those of the skew. An immediate consequence is one-to-one correspondence between absolutely continuous invariant measures (acims) for the position dependent random map and acims for its deterministic representation.
    Mathematics Subject Classification: Primary 37A05, 37E05.

    Citation:
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