Rigorous numerical Estimation of Lyapunov exponents and Invariant Measures of Iterated Function Systems and Random Matrix Products

@article{Froyland2000RigorousNE,
  title={Rigorous numerical Estimation of Lyapunov exponents and Invariant Measures of Iterated Function Systems and Random Matrix Products},
  author={Gary Froyland and Kazuyuki Aihara},
  journal={I. J. Bifurcation and Chaos},
  year={2000},
  volume={10},
  pages={103-122}
}
We present a fast, simple matrix method of computing the unique invariant measure and associated Lyapunov exponents of a nonlinear iterated function system. Analytic bounds for the error in our approximate invariant measure (in terms of the Hutchinson metric) are provided, while convergence of the Lyapunov exponent estimates to the true value is assured. As a special case, we are able to rigorously estimate the Lyapunov exponents of an iid random matrix product. Computation of the Lyapunov… CONTINUE READING

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