Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Study of the Continuous and Discrete Gambier Systems   We present a systematic study of the Gambier system, which in the continuous
case is given by two Riccati equations in cascade. We derive the condition for
its integrability and show that the generic Gambier system contains one free
function. We also derive the Schlesinger transformations for this system which
allows in principle the systematic construction of the integrable cases. The
above procedure is carried over to a discrete setting. We show thus how the
discrete Gambier system can be expressed as a system of two homographic
mappings in cascade. The integrable cases are obtained through the singularity
confinement discrete integrability criterion. Finally the discrete Schlesinger
transformations are also derived giving a handle to the construction of the
integrable Gambier mapping.

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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th