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Author: Gordon Wassermann
Publisher: Springer
ISBN: 3540384235
Category : Mathematics
Languages : en
Pages : 173
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Book Description
Author: Gordon Wassermann
Publisher: Springer
ISBN: 3540384235
Category : Mathematics
Languages : en
Pages : 173
Get Book Here
Book Description
Author: P. Hilton
Publisher: Springer
ISBN: 3540382542
Category : Mathematics
Languages : en
Pages : 415
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Book Description
This is a progress report on an experimental program, begun a year ago, in the exploration of resonant furcations (= catastrophes) by analog simulation and direct observation - the macroscope program.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 228
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Book Description
Author: C.G. Gibson
Publisher: Springer
ISBN: 3540379576
Category : Mathematics
Languages : en
Pages : 160
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Book Description
During the academic year 1974-75, the Department of Pure Mathematics in the University of Liverpool held a seminar on the topological stability of smooth mappings. The main objective was to piece together a complete proof of the topological stability theorem (conjectured by René Thom in 1960, and proved by John Mather in 1970) for which no published accounts existed. This volume comprises a write-up of the seminar by four of the participants. Any mathematician working in this area is conscious of a debt to the inventiveness of Thom, and to Mather for the technical work which placed much that was conjecture on firm mathematical foundations. The proof presented in these notes follows Thom's indications closely, and requires no more than some familiarity with differential topology and commutative algebra of the reader.
Author: James Damon
Publisher: American Mathematical Soc.
ISBN: 082182306X
Category : Mathematics
Languages : en
Pages : 102
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Book Description
In this paper we shall prove that two basic theorems of singularity theory, the versatility theorem and the finite determinacy theorem, are valid for a large class of equivalence relations on germs of mappings.
Author: Marta Bunge
Publisher: Cambridge University Press
ISBN: 110856335X
Category : Mathematics
Languages : en
Pages : 235
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Book Description
This book formally introduces synthetic differential topology, a natural extension of the theory of synthetic differential geometry which captures classical concepts of differential geometry and topology by means of the rich categorical structure of a necessarily non-Boolean topos and of the systematic use of logical infinitesimal objects in it. Beginning with an introduction to those parts of topos theory and synthetic differential geometry necessary for the remainder, this clear and comprehensive text covers the general theory of synthetic differential topology and several applications of it to classical mathematics, including the calculus of variations, Mather's theorem, and Morse theory on the classification of singularities. The book represents the state of the art in synthetic differential topology and will be of interest to researchers in topos theory and to mathematicians interested in the categorical foundations of differential geometry and topology.
Author: Domencio Castrigiano
Publisher: CRC Press
ISBN: 0429981430
Category : Mathematics
Languages : en
Pages : 306
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Book Description
Catastrophe Theory was introduced in the 1960s by the renowned Fields Medal mathematician René Thom as a part of the general theory of local singularities. Since then it has found applications across many areas, including biology, economics, and chemical kinetics. By investigating the phenomena of bifurcation and chaos, Catastrophe Theory proved to
Author: David Mond
Publisher: Springer Nature
ISBN: 3030344401
Category : Mathematics
Languages : en
Pages : 572
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Book Description
The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic. By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.
Author: Michele Matzeu
Publisher: Springer Science & Business Media
ISBN: 1461225701
Category : Mathematics
Languages : en
Pages : 542
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Book Description
Topological tools in Nonlinear Analysis had a tremendous develop ment during the last few decades. The three main streams of research in this field, Topological Degree, Singularity Theory and Variational Meth ods, have lately become impetuous rivers of scientific investigation. The process is still going on and the achievements in this area are spectacular. A most promising and rapidly developing field of research is the study of the role that symmetries play in nonlinear problems. Symmetries appear in a quite natural way in many problems in physics and in differential or symplectic geometry, such as closed orbits for autonomous Hamiltonian systems, configurations of symmetric elastic plates under pressure, Hopf Bifurcation, Taylor vortices, convective motions of fluids, oscillations of chemical reactions, etc . . . Some of these problems have been tackled recently by different techniques using equivariant versions of Degree, Singularity and Variations. The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in Nonlinear Analysis during the last two-three decades. The survey articles presented here reflect the personal taste and points of view of the authors (all of them well-known and distinguished specialists in their own fields) on the subject matter. A common feature of these papers is that of start ing with an historical introductory background of the different disciplines under consideration and climbing up to the heights of the most recent re sults.
Author: Wolfgang Wildgen
Publisher: John Benjamins Publishing
ISBN: 902725043X
Category : Language Arts & Disciplines
Languages : en
Pages : 294
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Book Description
The general topic of this book is the development of a realistic model of meaning; it has to account for the ecological basis of meaning in perception, action, and interaction, and is realistic in the sense of scientific realism, i.e. it is based on the most successful paradigm of modern science: dynamical systems theory. In Part One a model of sentences is put forward. The first chapter outlines the philosophical background of a theory of meaning. Chapter 2 gives a very short summary of recent proposals for a semantic model which considers image-like schemata. In Chapter 3 a realistic model of valence and basic predication is developed in detail. Chapter 4 treats multistability in meaning and the application of chaos theory and dissipative structures in semantics. Chapter 5 outlines the global framework of a stratified universe of meanings, and Chapter 6 prepares the way for Part Two: the analysis of narrative texts. Oral narratives of personal experience are the prototypical form in which experienced events are organized with the aim of remaking a piece of reality. In Chapter 7 a discrete grammar based on vectorial schemata is developed. Chapters 8 and 9 elaborate the syntax of narratives in Chapter 7. Chapter 10 progress to conversational dynamics.
