Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $C^\infty$ symplectic invariants of parabolic orbits and flaps in
  integrable Hamiltonian systems   In the present paper, we consider a smooth $C^\infty$ symplectic
classification of Lagrangian fibrations near cusp singularities, parabolic
orbits and cuspidal tori. We show that for these singularities as well as for
an arrangement of singularities known as a flap, which arises in the integrable
subcritical Hamiltonian Hopf bifurcation, the action variables form a complete
set of $C^\infty$ symplectic invariants. We also give a symplectic
classification for parabolic orbits in the real-analytic case. Namely, we prove
that a complete symplectic invariant in this case is given by a real-analytic
function germ in two variables. Additionally, we construct several symplectic
normal forms in the $C^\infty$ and/or real-analytic categories, including
real-analytic right and right-left symplectic normal forms for parabolic
orbits.

31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
18
The categories of this paper are: econ
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph