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Dichotomy and Integral Manifolds. Part I: General Principles

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This paper deals with two properties of an ordinary differential equation which are linked with each other: The dichotomy of the linearized differential equation (evaluated along trajectories) and the existence of integral manifolds. The differenceof our results compared with the ones existing in the literature concern the local/global aspect: Dichotomy is expressed in local coordinates (which may vary from point to point), the notion “integral manifold” is understood in the geometric sense (as a global manifold). The method is different from the standard one in so far as we introduce as a new analytic tool the discussion of two-point-boundary value problems.

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Authors and Affiliations

  1. Mathem. Institut Am Hubland, Universität Würzburg, 8700, Würzburg

    H. W. Knobloch

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  1. H. W. Knobloch
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Supported by Deutsche Forschungsgemeinschaft — Kn 164/3-1

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Knobloch, H.W. Dichotomy and Integral Manifolds. Part I: General Principles. Results. Math. 14, 93–124 (1988). https://doi.org/10.1007/BF03323219

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  • DOI: https://doi.org/10.1007/BF03323219

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