Invariant measures for Chebyshev maps. (2001)

• Record Type: Journal Article
• Authors: Boyarsky, Abraham; Góra, Paweł
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 14:Number 3(2001)
• Page Start: 257
• Page End: 264
• Publication Date: 2001
• Subjects: Chebyshev map -- absolutely continuous invariant measure -- Markov map; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953301000211
• Languages: English
• ISSNs: 1048-9533

Abstract

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.