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| Author | : James Damon |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 121 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : 082182452X |
In this paper we shall prove two theorems which together allow the infinitesimal methods of Thom and Mather in singularity theory to be applied to problems of topological equivalence of mappings.
| Author | : James Damon |
| Publisher | : Springer |
| Total Pages | : 255 |
| Release | : 2016-09-30 |
| Genre | : Mathematics |
| ISBN | : 3319414712 |
This monograph considers a basic problem in the computer analysis of natural images, which are images of scenes involving multiple objects that are obtained by a camera lens or a viewer’s eye. The goal is to detect geometric features of objects in the image and to separate regions of the objects with distinct visual properties. When the scene is illuminated by a single principal light source, we further include the visual clues resulting from the interaction of the geometric features of objects, the shade/shadow regions on the objects, and the “apparent contours”. We do so by a mathematical analysis using a repertoire of methods in singularity theory. This is applied for generic light directions of both the “stable configurations” for these interactions, whose features remain unchanged under small viewer movement, and the generic changes which occur under changes of view directions. These may then be used to differentiate between objects and determine their shapes and positions.
| Author | : Victor Goryunov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 218 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821853597 |
"This volume is a collection of papers presented at the 11th International Workshop on Real and Complex Singularities, held July 26-30, 2010, in Sao Carlos, Brazil, in honor of David Mond's 60th birthday. This volume reflects the high level of the conference discussing the most recent results and applications of singularity theory. Articles in the first part cover pure singularity theory: invariants, classification theory, and Milnor fibres. Articles in the second part cover singularities in topology and differential geometry, as well as algebraic geometry and bifurcation theory: Artin-Greenberg function of a plane curve singularity, metric theory of singularities, symplectic singularities, cobordisms of fold maps, Goursat distributions, sections of analytic varieties, Vassiliev invariants, projections of hypersurfaces, and linearity of the Jacobian ideal."--P. [4] of cover.
| Author | : Thomas J. Bridges |
| Publisher | : Springer |
| Total Pages | : 227 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540480404 |
The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate students in the areas of symplectic maps, Hamiltonian systems, singularity theory and equivariant bifurcation theory.
| Author | : Shyuichi Izumiya |
| Publisher | : World Scientific |
| Total Pages | : 383 |
| Release | : 2015-10-29 |
| Genre | : Mathematics |
| ISBN | : 9814590460 |
Differential Geometry from a Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wavefronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces.
| Author | : Jean-Paul Brasselet |
| Publisher | : Cambridge University Press |
| Total Pages | : 440 |
| Release | : 1994-07-07 |
| Genre | : Mathematics |
| ISBN | : 9780521466318 |
This book contains papers given at the International Singularity Conference held in 1991 at Lille.
| Author | : Bill Bruce |
| Publisher | : Cambridge University Press |
| Total Pages | : 468 |
| Release | : 1999-06-03 |
| Genre | : Computers |
| ISBN | : 9780521658881 |
An up-to-date survey of research in singularity theory.
| Author | : David Mond |
| Publisher | : Springer Nature |
| Total Pages | : 572 |
| Release | : 2020-01-23 |
| Genre | : Mathematics |
| ISBN | : 3030344401 |
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 | : Mark Roberts |
| Publisher | : Springer |
| Total Pages | : 329 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540470476 |
A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.
| Author | : Henk Broer |
| Publisher | : Springer |
| Total Pages | : 178 |
| Release | : 2003-01-01 |
| Genre | : Mathematics |
| ISBN | : 354036398X |
The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.
