Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: {\alpha}-limit sets and Lyapunov function for maps with one topological
  attractor   We consider the topological behaviors of continuous maps with one topological
attractor on compact metric space $X$. This kind of map is a generalization of
maps such as topologically expansive Lorenz map, unimodal map without
homtervals and so on. We provide a leveled $A$-$R$ pair decomposition for such
maps, and characterize $\alpha$-limit set of each point. Based on weak Morse
decomposition of $X$, we construct a bounded Lyapunov function $V(x)$, which
give a clear description of orbit behavior of each point in $X$ except a meager
set.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org