LEADER 04095nam 22006375 450 001 996466522203316 005 20200706093823.0 010 $a3-319-66526-X 024 7 $a10.1007/978-3-319-66526-9 035 $a(CKB)4100000000882282 035 $a(DE-He213)978-3-319-66526-9 035 $a(MiAaPQ)EBC5591096 035 $a(PPN)220120994 035 $a(EXLCZ)994100000000882282 100 $a20171015d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPainlevé III: A Case Study in the Geometry of Meromorphic Connections$b[electronic resource] /$fby Martin A. Guest, Claus Hertling 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XII, 204 p. 12 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2198 311 $a3-319-66525-1 320 $aIncludes bibliographical references and index. 327 $a1. 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. 330 $aThe purpose of this monograph is two-fold:  it introduces a conceptual language for the geometrical objects underlying Painlevé equations,  and it offers new results on a particular Painlevé III equation of type  PIII (D6), called PIII (0, 0, 4, ?4), describing its relation to isomonodromic families of vector bundles on P1  with meromorphic connections.  This equation is equivalent to the radial sine (or sinh) Gordon equation and, as such, it appears widely in geometry and physics.   It is used here as a very concrete and classical illustration of the modern theory of vector bundles with meromorphic connections. Complex multi-valued solutions on C* are the natural context for most of the monograph, but in the last four chapters real solutions on R>0 (with or without singularities) are addressed.  These provide examples of variations of TERP structures, which are related to  tt? geometry and harmonic bundles.    As an application, a new global picture of0 is given. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2198 606 $aDifferential equations 606 $aAlgebraic geometry 606 $aSpecial functions 606 $aFunctions of complex variables 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 615 0$aDifferential equations. 615 0$aAlgebraic geometry. 615 0$aSpecial functions. 615 0$aFunctions of complex variables. 615 14$aOrdinary Differential Equations. 615 24$aAlgebraic Geometry. 615 24$aSpecial Functions. 615 24$aFunctions of a Complex Variable. 676 $a515.352 700 $aGuest$b Martin A$4aut$4http://id.loc.gov/vocabulary/relators/aut$067285 702 $aHertling$b Claus$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466522203316 996 $aPainlevé III: A Case Study in the Geometry of Meromorphic Connections$91964434 997 $aUNISA