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020 _a9783319287362
_9978-3-319-28736-2
024 7 _a10.1007/978-3-319-28736-2
_2doi
050 4 _aQA372
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.352
_223
100 1 _aMitschi, Claude.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aDivergent Series, Summability and Resurgence I
_h[electronic resource] :
_bMonodromy and Resurgence /
_cby Claude Mitschi, David Sauzin.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXXI, 298 p. 24 illus., 19 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
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 _aDifferential Equations.
650 0 _aSequences (Mathematics).
650 0 _aFunctional equations.
650 0 _aDifferentiable dynamical systems.
650 0 _aTopological Groups.
650 1 4 _aOrdinary Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12147
650 2 4 _aSequences, Series, Summability.
_0http://scigraph.springernature.com/things/product-market-codes/M1218X
650 2 4 _aDifference and Functional Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12031
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
650 2 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
700 1 _aSauzin, David.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319287355
776 0 8 _iPrinted edition:
_z9783319287379
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2153
856 4 0 _uhttps://doi.org/10.1007/978-3-319-28736-2
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11442
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