Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic and Puiseux series solutions of systems of autonomous
  algebraic ODEs of dimension one in several variables   In this paper we study systems of autonomous algebraic ODEs in several
differential indeterminates. We develop a notion of algebraic dimension of such
systems by considering them as algebraic systems. Afterwards we apply
differential elimination and analyze the behavior of the dimension in the
resulting Thomas decomposition. For such systems of algebraic dimension one, we
show that all formal Puiseux series solutions can be approximated up to an
arbitrary order by convergent solutions. We show that the existence of Puiseux
series and algebraic solutions can be decided algorithmically. Moreover, we
present a symbolic algorithm to compute all algebraic solutions. The output can
either be represented by triangular systems or by their minimal polynomials.

32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga