An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence

@inproceedings{Junge2001AnAS,
  title={An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence},
  author={Oliver Junge},
  year={2001}
}
  • Oliver Junge
  • Published 2001
  • Mathematics
  • We prove convergence of a recently introduced adaptive multilevel algorithm for the efficient computation of invariant measures and attractors of dynamical systems. The proof works in the context of (sufficiently regular) stochastic processes and essentially shows that the discretization of phase space leads to a small random perturbation of the original process. A generalized version of a lemma of Khasminskii then gives the desired result. 

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    Figures and Tables from this paper.

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 10 CITATIONS

    Statistically optimal almost-invariant sets

    VIEW 4 EXCERPTS
    CITES BACKGROUND
    HIGHLY INFLUENCED

    Relatively Coherent Sets as a Hierarchical Partition Method

    Discretization of the Frobenius-Perron Operator Using a Sparse Haar Tensor Basis: The Sparse Ulam Method

    VIEW 1 EXCERPT
    CITES BACKGROUND

    Probabilistic Properties of Delay Differential Equations

    VIEW 1 EXCERPT
    CITES METHODS

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 22 REFERENCES

    ARPACK users' guide

    • Lehoucq
    • Society for Industrial and Applied Mathematics (SIAM)
    • 1998

    ARPACK users’ guide. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA. Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods

    • Lehoucq et al, R. B. 1998 Lehoucq, D. C. Sorensen, C. Yang
    • 1998

    Discrete approximation of invariant densities

    • S. M. Ulam
    • 1997