The emergence of singularity theory marks the return of mathematics to the study of the simplest analytical objects: functions, graphs, curves, surfaces. The modern singularity theory for smooth mappings, which is currently undergoing intensive development, can be thought of as a crossroad where the most abstract topics (such as algebraic and differential geometry topology, complex analysis, invariant theory, and Lie group theory) meet the most applied topics (such as dynamical systems, mathematical physics, geometrical optics, mathematical economics, and control theory). The papers in this volume include reviews of established areas as well as presentations of recent results in singularity theory.The authors have paid special attention to examples and discussion of results rather than burying the ideas in formalism, notation, and technical details. The aim is to introduce all mathematicians - as well as physicists, engineers, and other consumers of singularity theory - to the world of ideas and methods in this burgeoning area.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
Maße
Höhe: 255 mm
Breite: 175 mm
Gewicht
ISBN-13
978-0-8218-7502-5 (9780821875025)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
Period maps connected with a versal deformation of a critical point of a function, and the discriminant by A. N. Varchenko Characteristic classes of singularities by V. A. Vassiliev Lacunas of hyperbolic partial differential operators and singularity theory by V. A. Vassiliev Reflection groups in singularity theory by A. B. Givental Qualitative analysis of singularly perturbed systems of chemical kinetics by V. M. Goldshtein and V. A. Sobolev Bifurcations with symmetries by V. V. Goryunov Stratifications of function space and algebraic $K$-theory by S. M. Gusein-Zade Singularities in optimization problems by A. A. Davydov Nice dimensions and their generalizations in singularity theory by V. M. Zakalyukin On an inverse problem of measure theory by V. M. Klimkin Classes of coefficients of convergent random series in spaces $L_p,q$ by S. Ya. Novikov Corner singularities and multidimensional folds in nonlinear analysis by Yu. I. Sapronov Newton polyhedra (algebra and geometry) by A. G. Khovanskii.
