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Canonical forms of ordinary linear differential equations. (English) Zbl 0672.34005

Author’s abstract: A solution of two classical Halphen’s problem of equivalence and classification of OLDE is given. Transformation theory of the n-th order OLDE is constructed on algebraic base using the method of factorization of differential operators. Invariants of OLDE are obtained as consistent conditions of overdetermined system of nonlinear algebraic differential equations. The differential Euclidean algorithm and differential resultant are introduced and used. Representations for iterative equations are given by means of factorization of self-adjoints OLDE. The one-to-one correspondence of the canonical Halphen and Forsyth forms is found. There is pointed a connection between problems of equivalence and classification of OLDE and those of integrating linear and associated nonlinear equations.
Reviewer: M.Shahin

MSC:

34A30 Linear ordinary differential equations and systems
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34A05 Explicit solutions, first integrals of ordinary differential equations
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