Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regular flat structure and generalized Okubo system   We study a relationship between regular flat structures and generalized Okubo
systems. We show that the space of variables of isomonodromic deformations of a
regular generalized Okubo system can be equipped with a flat structure. As its
consequence, we introduce flat structures on the spaces of independent
variables of generic solutions to (classical) Painlev\'e equations (except for
PI). In our framework, the Painlev\'e equations PVI-PII can be treated
uniformly as just one system of differential equations called the
four-dimensional extended WDVV equation. Then the well-known coalescence
cascade of the Painlev\'e equations corresponds to the degeneration scheme of
the Jordan normal forms of a square matrix of rank four.

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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol