LEADER 03231cmm a2200457 i 4500 001 991003409249707536 007 cr cn ---mpcbr 008 170809s2016 de | o j |||| 0|eng d 020 $a9783319287362 024 7 $a10.1007/978-3-319-28736-2$2doi 035 $ab14329347-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a515.352$223 084 $aAMS 40-02 100 1 $aMitschi, Claude$0730104 245 10$aDivergent series, summability and resurgence I$h[e-book] :$bMonodromy and resurgence /$cby Claude Mitschi, David Sauzin 260 $aCham :$bSpringer,$c2016 300 $a1 online resource 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2153 505 0 $aPreface ; Preface to the three volumes. Part I: Monodromy in Linear Differential Equations ; 1 analytic continuation and monodromy ; Differential Galois Theory ; Inverse Problems ; The Riemann-Hilbert problem. Part II: Introduction to 1-Summability and Resurgence ; 5 Borel-Laplace Summation ; Resurgent Functions and Alien Calculus ; the Resurgent Viewpoint on Holomorphic Tangent-to-Identity Germs ; Acknowledgements ; Index 520 $aProviding an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh?s point of view. The second part expounds 1-summability and Ecalle?s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via ?alien calculus?, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra 650 0$aTopological groups 650 0$aLie groups 650 0$aDifference equations 650 0$aFunctional equations 650 0$aDynamics 650 0$aErgodic theory 650 0$aDifferential equations 650 0$aSequences (Mathematics) 700 1 $aSauzin, David$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0730103 710 2 $aSpringerLink (Online service) 776 08$iPrinted edition:$z9783319287355 856 40$uhttps://link.springer.com/book/10.1007/978-3-319-28736-2$zAn electronic book accessible through the World Wide Web 907 $a.b14329347$b03-03-22$c09-08-17 912 $a991003409249707536 996 $aDivergent series, summability and resurgence I$91748345 997 $aUNISALENTO 998 $ale013$b09-08-17$cm$d@ $e-$feng$gde $h0$i0