Aspects of Mathematics: A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev

Anosov, D. V.; Bolibruch, A. A.

This book is devoted to Hilbert's 21st problem (the Riemann-Hilbert problem) which belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concems the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this tumed out to be a rare case of a wrong forecast made by hirn. In 1989 the second author (A.B.) discovered a counterexample, thus 1 obtaining a negative solution to Hilbert's 21st problem. After we recognized that some "data" (singularities and monodromy) can be obtai­ ned from a Fuchsian system and some others cannot, we are enforced to change our point of view. To make the terminology more precise, we shaII caII the foIIowing problem the Riemann-Hilbert problem for such and such data: does there exist a Fuchsian system having these singularities and monodromy? The contemporary version of the 21 st Hilbert problem is to find conditions implying a positive or negative solution to the Riemann-Hilbert problem.

Details

Published by: Vieweg+Teubner Verlag

Publication Date: 2014-08-23

Format: Paperback

ISBN-13: 9783322929112

DOI: 10.1007/978-3-322-92909-9

Dimensions: 297cm x210cm

Pages: 193