The boundaries of singularity theory are broad and vague, connecting the most important applications of mathematics and science with more abstract areas. Optics, robotics, computer vision, Hamiltonian mechanics, bifurcation theory and differential equations are among the variety of topics that benefit from developments in the theory. With singularity theory encompassing more and more applications, Real and Complex Singularities provides insight into the future of this expanding field.
Comprising refereed contributions to the Fifth Workshop on Real and Complex Singularities, this volume addresses three important areas related to the broad subject of singularities. The first section deals with questions within singularity theory itself, representing the topics currently being investigated. The second explores applications of singularity theory to differential geometry, robotics, and computer vision. The final section consists of applications to bifurcation theory and dynamical systems.
With over two-hundred tables that provide quick access to data, this volume is a complete overview of the most current topics and applications of singularity theory. Real and Complex Singularities creates the opportunity for you to stay up-to-date with recent advances and discover promising directions for future research in the field.
Table of Contents
Weakly Whitney Stratified Sets
Plane Sections, Wf and Af
Wf and Integral Dependence
Coherent Vector Fields and Logarithmic Stratification
Very Good Quotients of Toric Varieties
Newton Polygon Relative to an Arc
A Two Colour Theorem and the Fundamental Class of a Polyhedron
Computation of the Thom Polynomial of ?1111 via Symmetries of Singularities
On the Classification of Multi-Germs of Maps from C2 to C3 under A-Equivalence
Flat Contact Singularities
Instantaneous Singular Sets Associated to Spatial Motions
Four-or-More-Vertex Theorems for Constant Curvature Manifolds
Affine Versions of the Symmetry Set
Bitangency Properties of Generic Closed Curves in Rn
Generic One-Parameter Families of Reversible Vector Fields
Counting Persistent Pitchforks
Controllability of a Generic Dynamic Inequality Near a Singular Point
Path Formulation and Forced Symmetry Breaking
Local Reversibility and Applications
On the Degeneracy of Planar Vector Fields