Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Singularities (Mathematics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In this short note, we first show (1) if (n, p) lies inside Mather's nice region then any A-stable multigerm f : (R^n, S)·(R^p, 0) and any C! unfolding of f are A-simple, and (2) for any (n, p) there exists a non-negative integer i such that for any integer j ((i·j)) there exists an A-stable multigerm f : (R^n·R^j, S · {0}) · (R^p · R^j , (0, 0)) which is not A-simple. Next, we obtain a characterization of curves among multigerms of corank at most one from the view point of A-stabie multigerms and A-simple multigerms. It turns out that for any (n, p) such that n < p an asymmetric Cantor set is naturally constructed by using upper bounds for multiplicities of A-stable multigerms and upper bounds for multiplicities of A-simple multigerms, and the desired characterization of curves can be obtained by cardinalities of constructed asymmetric Cantor sets.

Singularities (Mathematics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors cast the theory into a new light, that of singularity theory. This second edition has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added which covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory. Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities. The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus. Thus it will be invaluable for anyone who would like an introduction to modern singularity theory.

Singularities (Mathematics) --- Curves.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Differential equations --- Singularities (Mathematics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Differential equations. --- Singularities (Mathematics).