Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangian Formalism for nonlinear second-order Riccati Systems:
  one-dimensional Integrability and two-dimensional Superintegrability   The existence of a Lagrangian description for the second-order Riccati
equation is analyzed and the results are applied to the study of two different
nonlinear systems both related with the generalized Riccati equation. The
Lagrangians are nonnatural and the forces are not derivable from a potential.
The constant value $E$ of a preserved energy function can be used as an
appropriate parameter for characterizing the behaviour of the solutions of
these two systems. In the second part the existence of two--dimensional
versions endowed with superintegrability is proved. The explicit expressions of
the additional integrals are obtained in both cases. Finally it is proved that
the orbits of the second system, that represents a nonlinear oscillator, can be
considered as nonlinear Lissajous figures

30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph