Discretized ordinary differential equations and the Conley index |
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| Authors: | Marian Mrozek Krzysztof P Rybakowski |
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| Institution: | (1) Katedra Informatyki, Universytet Jagiellohski, ul. Kopernika 27, 31-501 Kraków, Poland;(2) Institut für Angewandte Mathematik, Universität Freiburg, Hermann-Herder-Stra e 10, 7800 Freiburg, Germany |
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| Abstract: | LetN be a compact isolating neighborhood of an isolated invariant setK with respect to an ODEx=f(x) (C) and (h) x=x + h (x, h) be a consistent one-step-discretization of (C). It is proved in this paper that for someh
0 > 0 and allh  ]0, h0, the setN isolates an invariant setK(h) of(h) and the discrete Conley index ofK(h) coincides with the continuous Conley index ofK. |
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| Keywords: | Discrete and continuous Conley index nontransversality measure one-step discretization |
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