Invariant measures for Chebyshev maps
Copyright policy )Invariant measures for Chebyshev maps
Let Tλ(x) = cos(λarccosx), −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 Tλ is determined exactly. This is accomplished by showing that Tλ is differentially conjugate to a piecewise linear Markov map whose unique invariant density can be computed as the unique left eigenvector of a matrix.
- Concordia University Wisconsin United States
- Concordia University Canada
Dynamical systems involving maps of the interval, Dynamical aspects of measure-preserving transformations, Chebyshev polynomial, Smooth ergodic theory, invariant measures for smooth dynamical systems
Dynamical systems involving maps of the interval, Dynamical aspects of measure-preserving transformations, Chebyshev polynomial, Smooth ergodic theory, invariant measures for smooth dynamical systems
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