Invariant measures for Chebyshev maps. (2001) - Boyarsky, Abraham; Góra, Paweł
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.