The Theory of Singularities and Its Applications

Author: V. I. Arnold

Publisher: Cambridge University Press


Category: Mathematics

Page: 72

View: 914

This book describes those singularities encountered in different branches of mathematics. The distinguished mathematician, Vladimir Arnold, avoids giving difficult proofs of all the results in order to provide the reader with a concise and accessible overview of the many guises and areas in which singularities appear. Some of these areas include geometry and optics, optimal control theory and algebraic geometry, reflection groups theory, dynamical systems theory, and the classical and quantum catastrophe theory.

Aesthetic Computing

Author: Paul A. Fishwick

Publisher: MIT Press


Category: Computers

Page: 457

View: 924

The application of the theory and practice of art to computer science: how aesthetics and art can play a role in computing disciplines.

Singularity Theory for Non-Twist KAM Tori

Author: A. González-Enríquez

Publisher: American Mathematical Soc.


Category: Mathematics

Page: 115

View: 619

In this monograph the authors introduce a new method to study bifurcations of KAM tori with fixed Diophantine frequency in parameter-dependent Hamiltonian systems. It is based on Singularity Theory of critical points of a real-valued function which the authors call the potential. The potential is constructed in such a way that: nondegenerate critical points of the potential correspond to twist invariant tori (i.e. with nondegenerate torsion) and degenerate critical points of the potential correspond to non-twist invariant tori. Hence, bifurcating points correspond to non-twist tori.

Dynamical Systems V

Bifurcation Theory and Catastrophe Theory

Author: V.I. Arnold

Publisher: Springer Science & Business Media


Category: Mathematics

Page: 274

View: 301

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.

Catastrophe Theory

Author: Vladimir I. Arnol'd

Publisher: Springer Science & Business Media


Category: Mathematics

Page: 150

View: 255

The new edition of this non-mathematical review of catastrophe theory contains updated results and many new or expanded topics including delayed loss of stability, shock waves, and interior scattering. Three new sections offer the history of singularity and its applications from da Vinci to today, a discussion of perestroika in terms of the theory of metamorphosis, and a list of 93 problems touching on most of the subject matter in the book.


Author: International Conference on Computer Vision



Category: Computer vision

Page: 1164

View: 397