%0 Journal Article 
%A Cano, José
%A Falkensteiner, Sebastian
%A Robertz, Daniel
%A Sendra Pons, Juan Rafael
%T Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables
%D 2022
%@ 0747-7171
%U http://hdl.handle.net/10017/51628
%X 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.
%K Algebraic autonomous ordinary differential equation
%K Puiseux series solution
%K Convergent solution
%K Artin approximation
%K Algebraic solution
%K Thomas decomposition
%K Matemáticas
%K Mathematics
%~ Biblioteca Universidad de Alcala