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Construction of systems of differential equations of Okubo normal form with rigid monodromy
Author(s) -
Yokoyama Toshiaki
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310364
Subject(s) - monodromy , mathematics , constant (computer programming) , simple (philosophy) , extension (predicate logic) , rank (graph theory) , matrix (chemical analysis) , monodromy matrix , diagonal , pure mathematics , representation (politics) , differential equation , mathematical analysis , combinatorics , geometry , eigenvalues and eigenvectors , philosophy , materials science , physics , epistemology , quantum mechanics , politics , computer science , political science , law , composite material , programming language
For systems of differential equations of the form ( xI n – T ) dy / dx = Ay (systems of Okubo normal form), where A is an n × n constant matrix and T is an n × n constant diagonal matrix, two kinds of operations (extension and restriction) are defined. It is shown that every irreducible system of Okubo normal form of semi‐simple type whose monodromy representation is rigid is obtained from a rank 1 system of Okubo normal form by a finite iteration of the operations. Moreover, an algorithm to calculate the generators of monodromy groups for rigid systems of Okubo normal form is given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)