International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2001 / Article

Open Access

Volume 14 |Article ID 326414 | 8 pages | https://doi.org/10.1155/S1048953301000211

Invariant measures for Chebyshev maps

Received01 Apr 2000
Revised01 Nov 2000

Abstract

Let Tλ(x)=cos(λarccosx), 1x1, 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 Tλ is determined exactly. This is accomplished by showing that Tλ is differentially conjugate to a piecewise linear Markov map whose unique invariant density can be computed as the unique left eigenvector of a matrix.

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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