Coupled Painleve V Systems in Dimension 4

Sasano, Yusuke

doi:10.1619/fesi.49.133

Cited by 6 publications

(7 citation statements)

References 4 publications

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“…In this section, we find an autonomous version of the degenerate Garnier system of type G (2,3) in two variables given by (79)…”

Section: In Two Variablesmentioning

confidence: 99%

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Symmetric Hamiltonian of the Garnier system and its degenerate systems in two variables

Sasano¹

2007

Preprint

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“…In this section, we find an autonomous version of the degenerate Garnier system of type G (2,3) in two variables given by (79)…”

Section: In Two Variablesmentioning

confidence: 99%

“….) ∈ C(t, s)[x, y, z, w], H 2 = π(H 1 ), where the transformation π is given by (3) π : (x, y, z, w, t, s) → (z, w, x, y, s, t), (π) 2 = 1 with some parameter's change, and the symbol H * (x, y, t; α 0 , . .…”

Section: Introductionmentioning

confidence: 99%

Symmetric Hamiltonian of the Garnier system and its degenerate systems in two variables

Sasano¹

2007

Preprint

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“…Let us review the notion of accessible singularity [4]. Let B be a connected open domain in C and π : W −→ B a smooth proper holomorphic map.…”

Section: Accessible Singularitymentioning

confidence: 99%

“…Let us recall the notion of local index [4]. When we construct the phase spaces of the higher order Painlevé equations, an object that we call the local index is the key for determining when we need to make a blowing-up of an accessible singularity or a blowing-down to a minimal phase space.…”

Section: Accessible Singularitymentioning

confidence: 99%

Resolution of Singularities for a Family of Third-Order Differential Systems With Small Meromorphic Solution Spaces

Sasano¹

2005

Kyushu J. Math.

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Abstract. Comparing the resolution of singularities for differential equations of Painlevé type, there are important differences between the second-order Painlevé equations and those of higher order. Unlike the second-order case, in higherorder cases there may exist some meromorphic solution spaces with codimension 2. In this paper, we will give an explicit global resolution of singularities for a 3-parameter family of third-order differential systems with meromorphic solution spaces of codimension 2. IntroductionIn 1979, Okamoto [1] constructed the spaces of initial conditions of Painlevé equations, which can be considered as the parametrized spaces of all solutions, including the meromorphic solutions. They are constructed by means of successive blowing-up procedures at singular points. For Painlevé equations, the dimension of the space of meromorphic solutions through any singular point is always codimension 1. However, in the case of higher-order Painlevé equations, the space of meromorphic solutions through a singular point may be of codimension greater than or equal to 2 [5]. In this paper, we will give an explicit resolution of singularities for a 3-parameter family of third-order differential systems with meromorphic solution spaces of codimension 2. For second-order Painlevé equations, we can obtain the entire space of initial conditions by adding subvarieties of codimension 1 (equivalently, of dimension 1) to the space of initial conditions of holomorphic solutions [3].

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“…→ (q 2 , p 2 , q 1 , p 1 , s, t; α 0 , α 1 , α 5 , α 3 , α 4 , α 2 ). (3) Here q 1 , p 1 , q 2 and p 2 denote unknown complex variables, and α 0 , α 1 , . .…”

Section: Introductionmentioning

confidence: 99%

Five-parameter family of partial differential systems in two variables

Sasano

2007

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Coupled Painleve V Systems in Dimension 4

Abstract: Abstract. We find and study coupled Painlevé V systems in dimension 4, which are di¤erent from the systems of type A 5 ð1Þ . We also give the augmented phase spaces for these systems.

Cited by 6 publications

References 4 publications

Symmetric Hamiltonian of the Garnier system and its degenerate systems in two variables

Symmetric Hamiltonian of the Garnier system and its degenerate systems in two variables

Resolution of Singularities for a Family of Third-Order Differential Systems With Small Meromorphic Solution Spaces

Five-parameter family of partial differential systems in two variables

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