Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rotation numbers of invariant manifolds around unstable periodic orbits
  for the diamagnetic Kepler problem   In this paper, a method to construct topological template in terms of
symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm
the topological template, rotation numbers of invariant manifolds around
unstable periodic orbits in a phase space are taken as an object of comparison.
The rotation numbers are determined from the definition and connected with
symbolic sequences encoding the periodic orbits in a reduced Poincar\'e
section. Only symbolic codes with inverse ordering in the forward mapping can
contribute to the rotation of invariant manifolds around the periodic orbits.
By using symbolic ordering, the reduced Poincar\'e section is constricted along
stable manifolds and a topological template, which preserves the ordering of
forward sequences and can be used to extract the rotation numbers, is
established. The rotation numbers computed from the topological template are
the same as those computed from their original definition.

1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas