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- W1943689034 abstract "We propose an $n$-dimensional analogue of elliptic difference Painleve equation. Some Weyl group acts on a family of rational varieties obtained by successive blow-ups at $m$ points in $mpp^n(mc)$, and in many cases they include the affine Weyl groups with symmetric Cartan matrices as subgroups. It is shown that the dynamical systems obtained by translations of these affine Weyl groups possess commuting flows and that their degrees grow quadratically. For the $E_7^{(1)}$ and $E_8^{(1)}$ cases, existence of preserved quantities is investigated. The elliptic difference case is also studied." @default.
- W1943689034 created "2016-06-24" @default.
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- W1943689034 date "2004-09-26" @default.
- W1943689034 modified "2023-09-27" @default.
- W1943689034 title "Integrability of $n$-dimensional dynamical systems of type $E_7^{(1)}$ and $E_8^{(1)}$" @default.
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