000 02927nam a22004935i 4500
001 978-3-540-44971-3
003 DE-He213
005 20160624101820.0
007 cr nn 008mamaa
008 121227s2000 gw | s |||| 0|eng d
020 _a9783540449713
_9978-3-540-44971-3
024 7 _a10.1007/BFb0104102
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aLombardi, Eric.
_eauthor.
245 1 0 _aOscillatory Integrals and Phenomena Beyond all Algebriac Orders
_h[electronic resource] :
_bWith Applications to Homoclinic Orbits in Reversible Systems /
_cby Eric Lombardi.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2000.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2000.
300 _aXVIII, 418 p.
_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 ;
_v1741
505 0 _a"Exponential tools" for evaluating oscillatory integrals -- Resonances of reversible vector fields -- Analytic description of periodic orbits bifurcating from a pair of simple purely imaginary eigenvalues -- Constructive floquet theory for periodic matrices near a constant one -- Inversion of affine equations around reversible homoclinic connections -- The 02+i? resonance -- The 02+i? resonance in infinite dimensions. Application to water waves -- The (i?0)2i?1 resonance.
520 _aDuring the last two decades, in several branches of science (water waves, crystal growth, travelling waves in one dimensional lattices, splitting of separatrices,...) different problems appeared in which the key point is the computation of exponentially small terms. This self-contained monograph gives new and rigorous mathematical tools which enable a systematic study of such problems. Starting with elementary illuminating examples, the book contains (i) new asymptotical tools for obtaining exponentially small equivalents of oscillatory integrals involving solutions of nonlinear differential equations; (ii) implementation of these tools for solving old open problems of bifurcation theory such as existence of homoclinic connections near resonances in reversible systems.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aPhysics.
650 0 _aEngineering.
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aComplexity.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540677857
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1741
856 4 0 _uhttp://dx.doi.org/10.1007/BFb0104102
942 _2EBK1296
_cEBK
999 _c30590
_d30590