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Invariant measures for Chebyshev maps

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  • Abraham Boyarsky
  • Paweł Góra

Abstract

Let T λ ( x ) = cos ( λ arccos x ) , − 1 ≤ x ≤ 1 , where λ > 1 is not an integer. For a certain set of λ 's which are irrational, the density of the unique absolutely continuous measure invariant under T λ is determined exactly. This is accomplished by showing that T λ is differentially conjugate to a piecewise linear Markov map whose unique invariant density can be computed as the unique left eigenvector of a matrix.

Suggested Citation

  • Abraham Boyarsky & Paweł Góra, 2001. "Invariant measures for Chebyshev maps," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-8, January.
    • Handle: RePEc:hin:jnijsa:326414
    DOI: 10.1155/S1048953301000211
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