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More on finite-time hyperbolicity

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Abstract

A solution of a nonautonomous ordinary differential equation is finite-time hyperbolic, i.e. hyperbolic on a compact interval of time, if the linearisation along that solution exhibits a strong exponential dichotomy. In analogy to classical asymptotic facts, it is shown that finite-time hyperbolicity is robust, that is, it persists under small perturbations. Eigenvalues and -vectors may be misleading with regards to hyperbolicity. This is demonstrated by means of simple examples.

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Authors and Affiliations

  1. Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada

    Arno Berger

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  1. Arno Berger
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Correspondence to Arno Berger.

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Berger, A. More on finite-time hyperbolicity. SeMA 51, 25–32 (2010). https://doi.org/10.1007/BF03322550

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  • DOI: https://doi.org/10.1007/BF03322550

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