LEADER 03152nam a2200421 i 4500 001 991003628049707536 006 m o d 007 cr cnu|||unuuu 008 190321s2017 sz a ob 001 0 eng d 020 $a9783319665269 020 $a331966526X 024 7 $a10.1007/978-3-319-66526-9 035 $ab14362491-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a515.355$223 084 $aAMS 34-02 084 $aAMS 32G20 084 $aAMS 34M55 100 1 $aGuest, Martin A.$067285 245 10$aPainlevé III :$ba case study in the geometry of Meromorphic connections$h[e-book] /$cMartin A. Guest, Claus Hertling 264 1$aCham :$bSpringer,$c2017 300 $a1 online resource (xii, 204 pages) :$billustrations 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2198 504 $aIncludes bibliographical references and index 505 0 $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 520 $aThe purpose of this monograph is two-fold:  it introduces a conceptual language for the geometrical objects underlying Painlevé equations,  and it offers new results on a particular Painlevé III equation of type  PIII (D6), called PIII (0, 0, 4, ?4), describing its relation to isomonodromic families of vector bundles on P1  with meromorphic connections.  This equation is equivalent to the radial sine (or sinh) Gordon equation and, as such, it appears widely in geometry and physics.   It is used here as a very concrete and classical illustration of the modern theory of vector bundles with meromorphic connections. Complex multi-valued solutions on C* are the natural context for most of the monograph, but in the last four chapters real solutions on R>0 (with or without singularities) are addressed.  These provide examples of variations of TERP structures, which are related to  tt? geometry and harmonic bundles. As an application, a new global picture of 0 is given 650 0$aPainlevé equations 700 1 $aHertling, Claus$eauthor$4http://id.loc.gov/vocabulary/relators/aut$066890 776 08$iPrinted edition:$z9783319665252 856 40$zAn electronic book accessible through the World Wide Web$uhttps://link.springer.com/book/10.1007/978-3-319-66526-9 907 $a.b14362491$b03-03-22$c21-03-19 912 $a991003628049707536 996 $aPainlevé III$91749801 997 $aUNISALENTO 998 $ale013$b21-03-19$cm$d@ $e-$feng$gsz $h0$i0