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

Michael Dellnitz; Oliver Junge

doi:10.1007/s007910050006

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

Michael Dellnitz, Oliver Junge

Universität Bayreuth

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

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.

Original language	English
Pages (from-to)	63-68
Number of pages	6
Journal	Computing and Visualization in Science
Volume	1
Issue number	2
DOIs	https://doi.org/10.1007/s007910050006
State	Published - 1998
Externally published	Yes

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10.1007/s007910050006

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title = "An adaptive subdivision technique for the approximation of attractors and invariant measures",

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.",

author = "Michael Dellnitz and Oliver Junge",

note = "Funding Information: ★Research of the authors is partly supported by the Deutsche Forschungsgemeinschaft under Grant De 448/5-2 and by the Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin.",

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PY - 1998

Y1 - 1998

N2 - 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.

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

Abstract

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