Autor(en)

Güttinger, W. and H. Eikemeier (eds.):

Sprache

Englisch

Gewicht

ca. 550 g

Bestell-Nr

1197953

Bemerkungen

Aus der Bibliothek von Prof. Wolfgang Haase, langjährigem Herausgeber der ANRW und des International Journal of the Classical Tradition (IJCT) / From the library of Prof. Wolfgang Haase, long-time editor of ANRW and the International Journal of the Classical Tradition (IJCT). - Einband leicht berieben und bestoßen, insgesamt guter Zustand / Binding slightly rubbed and bumped, overall good condition. - Introduction: The Symposia on Structural Stability in Physics had the objective to discuss recent applications of topological concepts deriving from the notion of structural stability -- notably, catastrophe and singularity theory -- in disparate physical systems exhibiting analogous behavior on different scales. The flow of ideas of the central lecture topics of this rapidly expanding field, which are at the frontier of current research, reflects the organization of these Proceedings: The first part of the book, GENERAL CONCEPTS, begins with R. Thom's reflections about the need for a revival of natural philosophy and the role catastrophe theory plays in it. E.C. Zeeman then summarizes the use of catastrophes for modeling in the sciences, and W. Glittinger provides a sketch of recent trends in applying catastrophe theory to physics. H. Haken closes out the chapter by linking synergetics with catastrophe and bifurcation theory. The book then turns, in the chapter on TOPOLOGICAL ASPECTS OF WAVE MOTION, to recent developments in the theory of random waves, fractals and diffraction catastrophes. This part starts with M.V. Berry's surveys of the roles catastrophes and fractals play in the theory of intensity fluctuations in random waves and in the distribution of modes in fractal resonators. J.F. Nye concludes the chapter with an analysis of stable optical caustics generated by irregular, shape-changing water drop lenses and the emerging umbilic diffraction patterns. The papers of the chapter on CATASTROPHES IN INFINITE DIMENSIONS deal with attempts to use catastrophe techniques in spaces with infinitely many dimensions, i.e., in continuum physics, and establish links with bifurcation theory. R. Magnus and T. Poston begin by showing in functional analytic terms how catastrophe theoretic methods can be used to gain insight into modeling infinite-dimensional systems. G. Dangelmayr analyzes bifurcation phenomena in variational problems by means of catastrophes. G. Dangelmayr, W. Giittinger and W. Veit then discuss semi- classical approximations of path integrals on and near caustics in terms of catastrophe theory. M.V. Berry concludes the chapter by analyzing the bifurcation of quantum bound states in the semiclassical limit using the notion of quantum maps. The contributions of the chapter on DEFECTS AND DISLOCATIONS center around the topological classification of singularities in ordered media, flow fields and wavefronts. R. Thom begins by developing new ideas about combining the notion of pseudogroup with catastrophe theory to describe stable defects in ordered media. J.F. Nye then discusses the changing topology of evolving flow fields, describes their structurally stable singularities in terms of catastrophes and applies the results to geophysical phenomena. F.J. Wright concludes the chapter by showing how catastrophe theory can be used to analyze and classify dislocations of wavefronts encountered in various branches of physics.

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