Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularities of Fredholm maps with one-dimensional kernels, II: Local
  behaviour and pointwise conditions   In analogy to what happens in finite dimensions we state the Normal Form
Theorem for k-singularities, introduced in the previous paper of the series. By
means of that we study the local behaviour near a singularity i.e. we deduce
local results of existence and multiplicity of solutions for the equation F(x)
= y where F is a 0-Fredholm map and x belongs to a suitable neighbourhood of a
singular point x_(o), once x_(o) is identified as one of the three kinds of
singularities defined in the first paper. To this end we also start to seek
alternative strategies for the determination of the type of a given singularity
according to our classification. Here we give a pointwise approach for
lower-order singularities which is coherent with the Thom-Boardman
classification in finite dimensions. We conclude by applying the pointwise
condition to a differential problem where, under suitable hypotheses, we
determine a swallow's tail singularity (3-singularity).

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The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph