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＜電子ブック＞
Painlevé III: A Case Study in the Geometry of Meromorphic Connections / by Martin A. Guest, Claus Hertling
(Lecture Notes in Mathematics. ISSN:16179692 ; 2198)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
大きさ	XII, 204 p. 12 illus : online resource
著者標目	*Guest, Martin A author Hertling, Claus author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Algebraic geometry LCSH:Special functions LCSH:Functions of complex variables FREE:Differential Equations FREE:Algebraic Geometry FREE:Special Functions FREE:Functions of a Complex Variable
一般注記	1. Introduction -- 2.- The Riemann-Hilbert correspondence for P3D6 bundles -- 3. (Ir)Reducibility -- 4. Isomonodromic families -- 5. Useful formulae: three 2 × 2 matrices --  6. P3D6-TEP bundles -- 7. P3D6-TEJPA bundles and moduli spaces of their monodromy tuples -- 8. Normal forms of P3D6-TEJPA bundles and their moduli spaces -- 9. Generalities on the Painleve´ equations -- 10. Solutions of the Painleve´ equation PIII (0, 0, 4, −4) -- 13. Comparison with the setting of Its, Novokshenov, and Niles -- 12.  Asymptotics of all solutions near 0 -- ...Bibliography. Index The purpose of this monograph is two-fold:  it introduces a conceptual language for the geometrical objects underlying Painlevé equations,  and it offers new results on a particular Painlevé III equation of type  PIII (D6), called PIII (0, 0, 4, −4), describing its relation to isomonodromic families of vector bundles on P1  with meromorphic connections.  This equation is equivalent to the radial sine (or sinh) Gordon equation and, as such, it appears widely in geometry and physics.   It is used here as a very concrete and classical illustration of the modern theory of vector bundles with meromorphic connections. Complex multi-valued solutions on C* are the natural context for most of the monograph, but in the last four chapters real solutions on R>0 (with or without singularities) are addressed.  These provide examples of variations of TERP structures, which are related to  tt∗ geometry and harmonic bundles.    As an application, a new global picture of0 is given HTTP:URL=https://doi.org/10.1007/978-3-319-66526-9

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