# Computing the invariant measure and the Lyapunov exponent for one-dimensional maps using a measure-preserving polynomial basis

@article{Aston2014ComputingTI,
title={Computing the invariant measure and the Lyapunov exponent for one-dimensional maps using a measure-preserving polynomial basis},
author={Philip J. Aston and Oliver Junge},
journal={Math. Comput.},
year={2014},
volume={83},
pages={1869-1902}
}
• Published 25 November 2011
• Mathematics, Computer Science
• Math. Comput.
We consider a generalisation of Ulam's method for approximating invariant densities of one-dimensional maps. Rather than use piecewise constant polynomials to approximate the density, we use polynomials of degree $n$ which are defined by the requirement that they preserve the measure on $n+1$ neighbouring subintervals. Over the whole interval, this results in a discontinuous piecewise polynomial approximation to the density. We prove error results where this approach is used to approximate…
3 Citations

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