Homoclinic connections and numerical integration |
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Authors: | Tovbis Alexander |
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Institution: | (1) Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364, USA |
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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.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | homoclinic connection numerical chaos finite difference methods 58F 65L |
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