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E-Books | Biblioteca da FCTUNL | Não Ficção | QA372.SPR FCT 97735 (Browse shelf) | 1 | Available |
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QA372.SPR FCT 97620 Topological structure of the solution set for evolution inclusions | QA372.SPR FCT 97648 Integral methods in science and engineering, Volume 1 | QA372.SPR FCT 97697 Analytic, algebraic and geometric aspects of differential equations | QA372.SPR FCT 97735 Painlevé III: A Case Study in the Geometry of Meromorphic Connections | QA372.SPR FCT 97765 Integral methods in science and engineering | QA372.SPR FCT 97779 Integrability of dynamical systems | QA372.SPR FCT 98031 Theory and applications of abstract semilinear cauchy problems |
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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.
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