LetTλ(x)=cos(λarccosx),?1≤x≤1, whereλ>1is not an integer. For a certain set ofλ's which are irrational, the density of the unique absolutely continuous measure invariant underTλis determined exactly. This is accomplished by showing thatTλis differentially conjugate to a piecewise linear Markov map whose unique invariant density can be computed as the unique left eigenvector of a matrix.
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