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On the Riemann–Hilbert Problem in Dimension 4

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Abstract

We consider the problem of existence of a Fuchsian system with a prescribed 4-dimensional monodromy. We give a classification of all cases of negative solution of this problem in terms of reducibility pattern of the representation, its local structure (which is described by a modification of Jordan form), and restrictions on asymptotics of solutions to Fuchsian systems in lower dimensions. We also show that realization of a reducible 4-dimensional representation by a Fucshian system, if it exists, can be chosen in a block upper-triangular form (though not necessarily with the same reducibility pattern). At the end of the paper, we present new counterexamples to the Riemann–Hilbert problem in dimension 4.

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Authors and Affiliations

  1. Yukos Oil Company, Moscow, Russia

    A. I. Gladyshev

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  1. A. I. Gladyshev
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Gladyshev, A.I. On the Riemann–Hilbert Problem in Dimension 4. Journal of Dynamical and Control Systems 6, 219–264 (2000). https://doi.org/10.1023/A:1009582120446

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  • DOI: https://doi.org/10.1023/A:1009582120446

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