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Homoclinic connections and numerical integration

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Abstract

One of the best known mechanisms of onset of chaotic motion is breaking of heteroclinic and homoclinic connections. It is well known that numerical integration on long time intervals very often becomes unstable (numerical instabilities) and gives rise to what is called “numerical chaos”. As one of the initial steps to discuss this phenomenon, we show in this paper that Euler's finite difference scheme does not preserve homoclinic connections.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, FL, 32816-1364, USA

    Alexander Tovbis

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  1. Alexander Tovbis
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Tovbis, A. Homoclinic connections and numerical integration. Numerical Algorithms 14, 261–267 (1997). https://doi.org/10.1023/A:1019121231815

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  • DOI: https://doi.org/10.1023/A:1019121231815

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