000 | 03988nam a22005535i 4500 | ||
---|---|---|---|
001 | 978-3-319-28736-2 | ||
003 | DE-He213 | ||
005 | 20190213151646.0 | ||
007 | cr nn 008mamaa | ||
008 | 160827s2016 gw | s |||| 0|eng d | ||
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 _d11442 |