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Integrability conditions for parameterized linear difference equations

Published: 26 June 2013 Publication History

Abstract

We study integrability conditions for systems of parameterized linear difference equations and related properties of linear differential algebraic groups. We show that isomonodromicity of such a system is equivalent to isomonodromicity with respect to each parameter separately under a linearly differentially closed assumption on the field of differential parameters. Due to our result, it is no longer necessary to solve non-linear differential equations to verify isomonodromicity, which will improve efficiency of computation with these systems. Moreover, it is not possible to further strengthen this result by removing the requirement on the parameters, as we show by giving a counterexample. We also discuss the relation between isomonodromicity and the properties of the associated parameterized difference Galois group.

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    cover image ACM Conferences
    ISSAC '13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation
    June 2013
    400 pages
    ISBN:9781450320597
    DOI:10.1145/2465506
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    Published: 26 June 2013

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    Author Tags

    1. difference algebra
    2. difference galois theory
    3. differential algebra
    4. differential algebraic groups
    5. integrability conditions

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