000			04822nam a22005655i 4500
001			978-0-8176-8343-6
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007			cr nn 008mamaa
008			120516s2012 xxu| s |||| 0|eng d
020			_a9780817683436 _9978-0-8176-8343-6
024	7		_a10.1007/978-0-8176-8343-6 _2doi
050		4	_aQA299.6-433
072		7	_aPBK _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515 _223
100	1		_aArnold, V.I. _eauthor.
245	1	0	_aSingularities of Differentiable Maps, Volume 2 _h[electronic resource] : _bMonodromy and Asymptotics of Integrals / _cby V.I. Arnold, S.M. Gusein-Zade, A.N. Varchenko.
264		1	_aBoston : _bBirkhäuser Boston : _bImprint: Birkhäuser, _c2012.
300			_aX, 492 p. 83 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aModern Birkhäuser Classics
505	0		_aPart I. The topological structure of isolated critical points of functions -- Introduction -- Elements of the theory of Picard-Lefschetz -- The topology of the non-singular level set and the variation operator of a singularity -- The bifurcation sets and the monodromy group of a singularity -- The intersection matrices of singularities of functions of two variables -- The intersection forms of boundary singularities and the topology of complete intersections -- Part II. Oscillatory integrals -- Discussion of results -- Elementary integrals and the resolution of singularities of the phase -- Asymptotics and Newton polyhedra -- The singular index, examples -- Part III. Integrals of holomorphic forms over vanishing cycles -- The simplest properties of the integrals -- Complex oscillatory integrals -- Integrals and differential equations -- The coefficients of series expansions of integrals, the weighted and Hodge filtrations and the spectrum of a critical point -- The mixed Hodge structure of an isolated critical point of a holomorphic function -- The period map and the intersection form -- References -- Subject Index.
520			_aOriginally published in the 1980s, Singularities of Differentiable Maps: Monodromy and Asymptotics of Integrals was the second of two volumes that together formed a translation of the authors' influential Russian monograph on singularity theory.  This uncorrected softcover reprint of the work brings its still-relevant content back into the literature, making it available—and affordable—to a global audience of researchers and practitioners. While the first volume of this title, subtitled Classification of Critical Points, Caustics and Wave Fronts, contained the zoology of differentiable maps—that is, was devoted to a description of what, where, and how singularities could be encountered—this second volume concentrates on elements of the anatomy and physiology of singularities of differentiable functions.  The questions considered here are about the structure of singularities and how they function. In the first part the authors consider the topological structure of isolated critical points of holomorphic functions: vanishing cycles; distinguished bases; intersection matrices; monodromy groups; the variation operator; and their interconnections and method of calculation.  The second part is devoted to the study of the asymptotic behavior of integrals of the method of stationary phase, which is widely met within applications.  The third and last part deals with integrals evaluated over level manifolds in a neighborhood of the critical point of a holomorphic function.   This monograph is suitable for mathematicians, researchers, postgraduates, and specialists in the areas of mechanics, physics, technology, and other sciences dealing with the theory of singularities of differentiable maps.
650		0	_aMathematics.
650		0	_aGeometry, algebraic.
650		0	_aTopological Groups.
650		0	_aGlobal analysis (Mathematics).
650		0	_aGlobal differential geometry.
650		0	_aCell aggregation _xMathematics.
650	1	4	_aMathematics.
650	2	4	_aAnalysis.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aDifferential Geometry.
650	2	4	_aTopological Groups, Lie Groups.
650	2	4	_aManifolds and Cell Complexes (incl. Diff.Topology).
650	2	4	_aApplications of Mathematics.
700	1		_aGusein-Zade, S.M. _eauthor.
700	1		_aVarchenko, A.N. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817683429
830		0	_aModern Birkhäuser Classics
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-8343-6
912			_aZDB-2-SMA
999			_c100250 _d100250