| 000 | 03855nam a22005535i 4500 | ||
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| 001 | 978-3-319-66526-9 | ||
| 003 | DE-He213 | ||
| 005 | 20181204134420.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 171015s2017 gw | s |||| 0|eng d | ||
| 020 |
_a9783319665269 _9978-3-319-66526-9 |
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| 024 | 7 |
_a10.1007/978-3-319-66526-9 _2doi |
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| 040 | _aISI Library, Kolkata | ||
| 050 | 4 | _aQA372 | |
| 072 | 7 |
_aPBKJ _2bicssc |
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| 072 | 7 |
_aMAT007000 _2bisacsh |
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_aPBKJ _2thema |
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| 082 | 0 | 4 |
_a515.352 _223 |
| 100 | 1 |
_aGuest, Martin A. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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| 245 | 1 | 0 |
_aPainlevé III: A Case Study in the Geometry of Meromorphic Connections _h[electronic resource] / _cby Martin A. Guest, Claus Hertling. |
| 264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2017. |
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| 300 |
_aXII, 204 p. 12 illus. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2198 |
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| 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 of0 is given. | ||
| 650 | 0 | _aDifferential Equations. | |
| 650 | 0 | _aGeometry, algebraic. | |
| 650 | 0 | _aFunctions, special. | |
| 650 | 0 | _aFunctions of complex variables. | |
| 650 | 1 | 4 |
_aOrdinary Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12147 |
| 650 | 2 | 4 |
_aAlgebraic Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M11019 |
| 650 | 2 | 4 |
_aSpecial Functions. _0http://scigraph.springernature.com/things/product-market-codes/M1221X |
| 650 | 2 | 4 |
_aFunctions of a Complex Variable. _0http://scigraph.springernature.com/things/product-market-codes/M12074 |
| 700 | 1 |
_aHertling, Claus. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783319665252 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783319665276 |
| 830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2198 |
|
| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-66526-9 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-LNM | ||
| 942 | _cEB | ||
| 950 | _aMathematics and Statistics (Springer-11649) | ||
| 999 |
_c427186 _d427186 |
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