Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrability of Lie systems through Riccati equations   Integrability conditions for Lie systems are related to reduction or
transformation processes. We here analyse a geometric method to construct
integrability conditions for Riccati equations following these approaches. This
approach provides us with a unified geometrical viewpoint that allows us to
analyse some previous works on the topic and explain new properties. Moreover,
this new approach can be straightforwardly generalised to describe
integrability conditions for any Lie system. Finally, we show the usefulness of
our treatment in order to study the problem of the linearisability of Riccati
equations.

28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin