Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stickiness in Chaos   We distinguish two types of stickiness in systems of two degrees of freedom
(a) stickiness around an island of stability and (b) stickiness in chaos, along
the unstable asymptotic curves of unstable periodic orbits. We studied these
effects in the standard map with a rather large nonlinearity K=5, and we
emphasized the role of the asymptotic curves U, S from the central orbit O and
the asymptotic curves U+U-S+S- from the simplest unstable orbit around the
island O1. We calculated the escape times (initial stickiness times) for many
initial points outside but close to the island O1. The lines that separate the
regions of the fast from the slow escape time follow the shape of the
asymptotic curves S+,S-. We explained this phenomenon by noting that lines
close to S+ on its inner side (closer to O1) approach a point of the orbit 4/9,
say P1, and then follow the oscillations of the asymptotic curve U+, and escape
after a rather long time, while the curves outside S+ after their approach to
P1 follow the shape of the asymptotic curves U- and escape fast into the
chaotic sea. All these curves return near the original arcs of U+,U- and
contribute to the overall stickiness close to U+,U-. The isodensity curves
follow the shape of the curves U+,U- and the maxima of density are along U+,U-.
For a rather long time the stickiness effects along U+,U- are very pronounced.
However after much longer times (about 1000 iterations) the overall stickiness
effects are reduced and the distribution of points in the chaotic sea outside
the islands tends to be uniform.

1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org