Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonautonomous Conley Index Theory: The Connecting Homomorphism   Attractor-repeller decompositions of isolated invariant sets give rise to
so-called connecting homomorphisms. These homomorphisms reveal information on
the existence and structure of connecting trajectories of the underlying
dynamical system.
  To give a meaningful generalization of this general principle to
nonautonomous problems, the nonautonomous homology Conley index is expressed as
a direct limit. Moreover, it is shown that a nontrivial connecting homomorphism
implies, on the dynamical systems level, a sort of uniform connectedness of the
attractor-repeller decomposition.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ