000 02823nam a22004935i 4500
001 978-3-540-35591-5
003 DE-He213
005 20190213151111.0
007 cr nn 008mamaa
008 100301s2006 gw | s |||| 0|eng d
020 _a9783540355915
_9978-3-540-35591-5
024 7 _a10.1007/3-540-35590-1
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
100 1 _aHoeven, Joris van der.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aTransseries and Real Differential Algebra
_h[electronic resource] /
_cby Joris van der Hoeven.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2006.
300 _aXII, 260 p. 8 illus.
_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 ;
_v1888
505 0 _aOrderings -- Grid-based series -- The Newton polygon method -- Transseries -- Operations on transseries -- Grid-based operators -- Linear differential equations -- Algebraic differential equations -- The intermediate value theorem.
520 _aTransseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.
650 0 _aGeometry, algebraic.
650 0 _aFunctional equations.
650 0 _aDifferentiable dynamical systems.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
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
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540825890
776 0 8 _iPrinted edition:
_z9783540355908
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1888
856 4 0 _uhttps://doi.org/10.1007/3-540-35590-1
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c9510
_d9510