Singularity theory / V.I. Arnold, V.V. Goryunov, O.V. Lyashko, ... [et al.]

Auteur secondaire : Goryunov, Viktor Vladimirovich (1968-) - Editeur scientifique ; Lyashko, Oleg V. - Editeur scientifique ; Arnold, Vladimir Igorevich (1937-2010) - Editeur scientifiqueType de document: Livre numériqueCollection: Encyclopaedia of mathematical sciences ; 6Langue: anglaisÉditeur: Berlin : Springer, 1998 ISBN: 9783642580093 Note: The first edition of this book appeared as “Dynamical systems VI” in the “Encycl. Math. Sci. 6 (1993)”. The Russian original appeared as “Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 6 (1988)”. The book contains four chapters: “Critical points of functions”, “Monodromy groups of critical points”, “Basic properties of maps”, and “The global theory of singularities”. It has illustrative examples, a very good bibliography, and it should be in the personal library of every mathematician or physicist interested in modern mathematical analysis. Sujets MSC: 58C25 Global analysis, analysis on manifolds -- Calculus on manifolds; nonlinear operators -- Differentiable maps
58Kxx Global analysis, analysis on manifolds -- Theory of singularities and catastrophe theory
58E05 Global analysis, analysis on manifolds -- Variational problems in infinite-dimensional spaces -- Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
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The first edition of this book appeared as “Dynamical systems VI” in the “Encycl. Math. Sci. 6 (1993)”. The Russian original appeared as “Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 6 (1988)”.

The book contains four chapters: “Critical points of functions”, “Monodromy groups of critical points”, “Basic properties of maps”, and “The global theory of singularities”. It has illustrative examples, a very good bibliography, and it should be in the personal library of every mathematician or physicist interested in modern mathematical analysis.

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