Abraham Boyarsky, Paweł Góra, "Invariant measures for Chebyshev maps", International Journal of Stochastic Analysis, vol. 14, Article ID 326414, 8 pages, 2001. https://doi.org/10.1155/S1048953301000211
Invariant measures for Chebyshev maps
Let , , where is not an integer. For a certain set of 's which are irrational, the density of the unique absolutely continuous measure invariant under is determined exactly. This is accomplished by showing that is 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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