Invariant measures for Chebyshev maps

Abraham Boyarsky and Paweł Góra

International Journal of Stochastic Analysis, 2001, vol. 14, 1-8

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.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:326414

DOI: 10.1155/S1048953301000211

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