04854nam 22007575 450 99646648080331620200704233538.03-642-31695-610.1007/978-3-642-31695-1(CKB)3400000000102751(SSID)ssj0000788854(PQKBManifestationID)11462938(PQKBTitleCode)TC0000788854(PQKBWorkID)10828719(PQKB)10974478(DE-He213)978-3-642-31695-1(MiAaPQ)EBC3070963(PPN)16832007X(EXLCZ)99340000000010275120121009d2013 u| 0engurnn|008mamaatxtccrIntroduction to Stokes Structures[electronic resource] /by Claude Sabbah1st ed. 2013.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2013.1 online resource (XIV, 249 p. 14 illus., 1 illus. in color.) Lecture Notes in Mathematics,0075-8434 ;2060Bibliographic Level Mode of Issuance: Monograph3-642-31694-8 Includes bibliographical references and index.1.T-filtrations --2.Stokes-filtered local systems in dimension one --3.Abelianity and strictness --4.Stokes-perverse sheaves on Riemann surfaces --5.The Riemann-Hilbert correspondence for holonomic D-modules on curves --6.Applications of the Riemann-Hilbert correspondence to holonomic distributions --7.Riemann-Hilbert and Laplace on the affine line (the regular case) --8.Real blow-up spaces and moderate de Rham complexes --9.Stokes-filtered local systems along a divisor with normal crossings --10.The Riemann-Hilbert correspondence for good meromorphic connections (case of a smooth divisor) --11.Good meromorphic connections (formal theory) --12.Good meromorphic connections (analytic theory) and the Riemann-Hilbert correspondence --13.Push-forward of Stokes-filtered local systems --14.Irregular nearby cycles --15.Nearby cycles of Stokes-filtered local systems.This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.Lecture Notes in Mathematics,0075-8434 ;2060Algebraic geometryDifferential equationsApproximation theorySequences (Mathematics)Functions of complex variablesPartial differential equationsAlgebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Ordinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Approximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Sequences, Series, Summabilityhttps://scigraph.springernature.com/ontologies/product-market-codes/M1218XSeveral Complex Variables and Analytic Spaceshttps://scigraph.springernature.com/ontologies/product-market-codes/M12198Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Algebraic geometry.Differential equations.Approximation theory.Sequences (Mathematics).Functions of complex variables.Partial differential equations.Algebraic Geometry.Ordinary Differential Equations.Approximations and Expansions.Sequences, Series, Summability.Several Complex Variables and Analytic Spaces.Partial Differential Equations.516.35Sabbah Claudeauthttp://id.loc.gov/vocabulary/relators/aut311999BOOK996466480803316Introduction to Stokes structures241611UNISA