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

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Computing and Visualization in Science

Abstract.

Recently subdivision techniques have been introduced in the numerical investigation of the temporal behavior of dynamical systems. In this article we intertwine the subdivision process with the computation of invariant measures and propose an adaptive scheme for the box refinement which is based on the combination of these methods. Using this new algorithm the numerical effort for the computation of box coverings is in general significantly reduced, and we illustrate this fact by several numerical examples.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany ( http://www.uni-bayreuth.de/departments/math/˜mdellnitz; http://www.uni-bayreuth.de/departments/math/˜ojunge) , , , , , , DE

    Michael Dellnitz & Oliver Junge

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  1. Michael Dellnitz
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  2. Oliver Junge
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Received: 13 January 1997 / Accepted: 29 September 1997

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Dellnitz, M., Junge, O. An adaptive subdivision technique for the approximation of attractors and invariant measures. Comput Visual Sci 1, 63–68 (1998). https://doi.org/10.1007/s007910050006

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  • DOI: https://doi.org/10.1007/s007910050006

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