Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics on Hyperspaces   Given a compact metric space (X; \varrho) and a continuous function
f:X\rightarrow X, we study the dynamics of the induced map \bar{f} on the
hyperspace of the compact subsets of X. We show how the chain recurrent set of
f and its components are related with the one of the induced map. The main
result of the paper proves that, under mild conditions, the numbers of chain
components of \bar{f} is greater than the ones of f. Showing the richness in
the dynamics of \bar{f} which cannot be perceived by f.

3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th