LEADER 03435nam 2200553Ia 450 001 9910438153003321 005 20200520144314.0 010 $a3-642-31695-6 024 7 $a10.1007/978-3-642-31695-1 035 $a(CKB)3400000000102751 035 $a(SSID)ssj0000788854 035 $a(PQKBManifestationID)11462938 035 $a(PQKBTitleCode)TC0000788854 035 $a(PQKBWorkID)10828719 035 $a(PQKB)10974478 035 $a(DE-He213)978-3-642-31695-1 035 $a(MiAaPQ)EBC3070963 035 $a(PPN)16832007X 035 $a(EXLCZ)993400000000102751 100 $a20121007d2013 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to stokes structures /$fClaude Sabbah 205 $a1st ed. 2013. 210 $aBerlin $cSpringer$dc2013 215 $a1 online resource (XIV, 249 p. 14 illus., 1 illus. in color.) 225 1 $aLecture notes in mathematics,$x1617-9692 ;$v2060 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-31694-8 320 $aIncludes bibliographical references and index. 327 $g1.$tT-filtrations --$g2.$tStokes-filtered local systems in dimension one --$g3.$tAbelianity and strictness --$g4.$tStokes-perverse sheaves on Riemann surfaces --$g5.$tThe Riemann-Hilbert correspondence for holonomic D-modules on curves --$g6.$tApplications of the Riemann-Hilbert correspondence to holonomic distributions --$g7.$tRiemann-Hilbert and Laplace on the affine line (the regular case) --$g8.$tReal blow-up spaces and moderate de Rham complexes --$g9.$tStokes-filtered local systems along a divisor with normal crossings --$g10.$tThe Riemann-Hilbert correspondence for good meromorphic connections (case of a smooth divisor) --$g11.$tGood meromorphic connections (formal theory) --$g12.$tGood meromorphic connections (analytic theory) and the Riemann-Hilbert correspondence --$g13.$tPush-forward of Stokes-filtered local systems --$g14.$tIrregular nearby cycles --$g15.$tNearby cycles of Stokes-filtered local systems. 330 $aThis research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v2060. 606 $aDifferential equations, Linear 606 $aStokes' theorem 615 0$aDifferential equations, Linear. 615 0$aStokes' theorem. 676 $a515/.354 700 $aSabbah$b Claude$0311999 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438153003321 996 $aIntroduction to Stokes structures$9241611 997 $aUNINA