Invariant measures for Chebyshev maps

[摘要] 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.

[学科分类] 应用数学