Journal of Dynamical and Control Systems

, Volume 6, Issue 2, pp 219–264

On the Riemann–Hilbert Problem in Dimension 4

  • A. I. Gladyshev


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.

Riemann–Hilbert problem Fuchsian system monodromy representation 


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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • A. I. Gladyshev
    • 1
  1. 1.Yukos Oil CompanyMoscowRussia

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