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Computational complexity of iterated maps on the interval

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  • Spandl, Christoph

Abstract

The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. There are two main results. First, the computational complexity measure considered here is related to the Lyapunov exponent of the dynamical system under consideration. Second, the presented algorithm is optimal with regard to that complexity measure.

Suggested Citation

  • Spandl, Christoph, 2012. "Computational complexity of iterated maps on the interval," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1459-1477.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:8:p:1459-1477
    DOI: 10.1016/j.matcom.2012.02.003
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    Cited by:

    1. Nepomuceno, Erivelton G. & Rodrigues Junior, Heitor M. & Martins, Samir A.M. & Perc, Matjaž & Slavinec, Mitja, 2018. "Interval computing periodic orbits of maps using a piecewise approach," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 67-75.

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