RT info:eu-repo/semantics/article
T1 Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables
A1 Cano, José
A1 Falkensteiner, Sebastian
A1 Robertz, Daniel
A1 Sendra Pons, Juan Rafael
K1 Algebraic autonomous ordinary differential equation
K1 Puiseux series solution
K1 Convergent solution
K1 Artin approximation
K1 Algebraic solution
K1 Thomas decomposition
K1 Matemáticas
K1 Mathematics
AB In this paper we study systems of autonomous algebraic ODEsin several differential indeterminates. We develop a notion ofalgebraic dimension of such systems by considering them asalgebraic systems. Afterwards we apply differential eliminationand analyze the behavior of the dimension in the resultingThomas decomposition. For such systems of algebraic dimensionone, we show that all formal Puiseux series solutions can beapproximated up to an arbitrary order by convergent solutions. Weshow that the existence of Puiseux series and algebraic solutionscan be decided algorithmically. Moreover, we present a symbolicalgorithm to compute all algebraic solutions. The output caneither be represented by triangular systems or by their minimalpolynomials.
PB Elsevier
SN 0747-7171
YR 2022
FD 2022-04-22
LK http://hdl.handle.net/10017/51628
UL http://hdl.handle.net/10017/51628
LA eng
NO Agencia Estatal de Investigación
DS MINDS@UW
RD 03-jun-2023