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

  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.},
  • P. Aston, O. Junge
  • 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… 

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