Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of a compact operator   Let $T:X\to X$ be a compact linear (or more generally affine) operator from a
Banach space into itself. For each $x\in X$, the sequence of iterates $T^nx,
n=0,1,...$ and its averages $\frac{1}{k}\sum_{k=0}^nT^{k-1}x, n=0,1,...$ are
either bounded or approach infinity.

4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an