000			04609nam a22005655i 4500
001			978-0-8176-8340-5
003			DE-He213
005			20140220083228.0
007			cr nn 008mamaa
008			120523s2012 xxu| s |||| 0|eng d
020			_a9780817683405 _9978-0-8176-8340-5
024	7		_a10.1007/978-0-8176-8340-5 _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 1 _h[electronic resource] : _bClassification of Critical Points, Caustics and Wave Fronts / _cby V.I. Arnold, S.M. Gusein-Zade, A.N. Varchenko.
264		1	_aBoston : _bBirkhäuser Boston : _bImprint: Birkhäuser, _c2012.
300			_aXII, 282 p. 67 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. Basic concepts -- The simplest examples -- The classes Sigma^ I -- The quadratic differential of a map -- The local algebra of a map and the Weierstrass preparation theorem -- The local multiplicity of a holomorphic map -- Stability and infinitesimal stability -- The proof of the stability theorem -- Versal deformations -- The classification of stable germs by genotype -- Review of further results -- Part II. Critical points of smooth functions -- A start to the classification of critical points -- Quasihomogeneous and semiquasihomogeneous singularities -- The classification of quasihomogeneous functions -- Spectral sequences for the reduction to normal forms -- Lists of singularities -- The determinator of singularities -- Real, symmetric and boundary singularities -- Part III. Singularities of caustics and wave fronts -- Lagrangian singularities -- Generating families -- Legendrian singularities -- The classification of Lagrangian and Legendrian singularities -- The bifurcation of caustics and wave fronts -- References -- Further references -- Subject Index.
520			_aOriginally published in the 1980s, Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts was the first 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. Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science.  The three parts of this first volume deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities.  Building on these concepts, the second volume (Monodromy and Asymptotics of Integrals) describes the topological and algebro-geometrical aspects of the theory, including monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts accommodates the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level.  With this foundation, the book's sophisticated development permits readers to explore an unparalleled breadth of applications.
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: _z9780817683399
830		0	_aModern Birkhäuser Classics
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-8340-5
912			_aZDB-2-SMA
999			_c100249 _d100249