Space of initial conditions for the four-dimensional Fuji-Suzuki-Tsuda system

2020/11/12 by Takenawa, Tomoyuki · 2 citations
#14E07 #34M55 #37F10 #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.2011.06271

Abstract

A geometric study for an integrable 4-dimensional dynamical system so called the Fuji-Suzuki-Tsuda system is given. By the resolution of indeterminacy, the group of its Bäklund transformations is lifted to a group of pseudo-isomorphisms between rational varieties obtained from (P¹)⁴ by blowing-up along eight 2-dimensional subvarieties and four 1-dimensional subvarieties. The root basis is realised in the Néron-Severi bilattices. A discrete Painlevé system with quadratic degree growth is also realised as its translational element.

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• Initial value space of the fourth order Painlevé system with A₅⁽¹⁾× A₁⁽¹⁾ symmetry
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