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arXiv · 0704.2391

Ordinary differential systems in dimension three with affine Weyl group symmetry of types $D_4^{(1)},B_3^{(1)},G_2^{(1)},D_3^{(2)}$ and $A_2^{(2)}$

Yusuke Sasano
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Abstract

We present a four-parameter family of ordinary differential systems in dimension three with affine Weyl group symmetry of type $D_4^{(1)}$. By obtaining its first integral, we can reduce this system to the second-order non-linear ordinary differential equations of Painlevé type. We also study this system restricted its parameters. Each system can be obtained by connecting some invariant divisors in the system of type $D_4^{(1)}$. Each system admits affine Weyl group symmetry of types $B_3^{(1)},G_2^{(1)},D_3^{(2)}$ and $A_2^{(2)}$, respectively. These symmetries, holomorphy conditions and invariant divisors are new.

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Yusuke Sasano. 2009-12-14. Ordinary differential systems in dimension three with affine Weyl group symmetry of types $D_4^{(1)},B_3^{(1)},G_2^{(1)},D_3^{(2)}$ and $A_2^{(2)}$. https://arxiv.org/abs/0704.2391

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