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Yusuke Sasano

Publications and source records attributed to Yusuke Sasano.

34 records · Page 2Linked to original sources
arXiv2009

Coupled Painlevé systems with affine Weyl group symmetry of types $D_3^{(2)}$ and $D_5^{(2)}$

In this paper, we find a two-parameter family of coupled Painlevé systems in dimension four with affine Weyl group symmetry of type $D_3^{(2)}$. We also find a four-parameter family of 2-coupled $D_3^{(2)}$-systems in dimension eight with affine Weyl group symmetry of type $D_5^{(2)}$. We show that for each system, we give its symmetry and holomorphy conditions, respectively. These symmetries, holomorphy conditions and invariant divisors are new.

math.AG↗
arXiv2009

Coupled Painlevé systems with affine Weyl group symmetry of types $A_7^{(2)},A_5^{(2)}$ and $D_4^{(3)}$

We find a four-parameter family of coupled Painlevé VI systems in dimension four with affine Weyl group symmetry of type $A_7^{(2)}$. This is the first example which gave higher-order Painlevé equations of type $A_{2l+5}^{(2)}$. We then give an explicit description of a confluence process from this system to a 3-parameter family of coupled Painlevé V and III systems in dimension four with $W(A_5^{(2)})$-symmetry. For a degenerate system of $A_5^{(2)}$ system, we also find a two-parameter family of ordinary differential systems in dimension four with affine Weyl group symmetry of type $D_4^{(3)}$. This is the first example which gave higher-order Painlevé equations of type $D_4^{(3)}$. We show that for each system, we give its symmetry and holomorphy conditions. These symmetries, holomorphy conditions and invariant divisors are new.

math.AG↗
arXiv2009

Second order polynomial Hamiltonian systems with ${\tilde W}(E_6^{(1)}),{\tilde W}(E_7^{(1)})$ and $W(E_8^{(1)})$-symmetry

We find and study a six (resp. seven, eight)-parameter family of polynomial Hamiltonian systems of second order, respectively. This system admits the affine Weyl group symmetry of type $E_6^{(1)}$ (resp. $E_7^{(1)}, E_8^{(1)}$) as the group of its B{ä}cklund transformations. Each system is the first example which gave second-order polynomial Hamiltonian system with ${\tilde W}(E_6^{(1)})$ (resp. ${\tilde W}(E_7^{(1)}), W(E_8^{(1)})$)-symmetry. We also show that its space of initial conditions $S$ is obtained by gluing eight (resp. nine, ten) copies of ${\Bbb C}^2$ via the birational and symplectic transformations.

math.AG↗
arXiv2008

Four-dimensional Painlevé systems of types $D_5^{(1)}$ and $B_4^{(1)}$

We find and study a five-parameter family of four-dimensional coupled Painlevé V systems with affine Weyl group symmetry of type $D_5^{(1)}$. We then give an explicit description of a confluence from those systems to a four-parameter family of four-dimensional coupled Painlevé III systems with affine Weyl group symmetry of type $B_4^{(1)}$.

math.AG↗
arXiv2007

Studies on the Garnier system in two variables

We study some Hamiltonian structures of the Garnier system in two variables from the viewpoints of its symmetry and holomorphy properties. We also give a generalization of {\it Okamoto transformation \it}of the sixth Painlevé system.

math.AG↗
arXiv2007

Symmetries in the system of type $A_5^{(2)}$

In this paper, we propose a 3-parameter family of coupled Painlevé III systems in dimension four with affine Weyl group symmetry of type $A_5^{(2)}$. We also propose its symmetric form in which the $A_5^{(2)}$-symmetries become clearly visible.

math.AG↗
arXiv2007

Symmetries in the system of type $D_4^{(1)}$

In this paper, we propose a 4-parameter family of coupled Painlevé III systems in dimension four with affine Weyl group symmetry of type $D_4^{(1)}$. We also propose its symmetric form in which the $D_4^{(1)}$-symmetries become clearly visible.

math.AG↗