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 Torres, José María
A1 Sendra Pons, Juan Rafael
A1 Falkensteiner, Sebastian
A1 Robertz, Daniel
K1 Matemáticas
K1 Algebraic autonomous ordinary differential equation Puiseux series solution Convergent solution Artin approximation Algebraic solution Thomas decomposition
K1 1201 Álgebra
K1 1204 Geometría
AB 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.
PB Springer
SN 0747-7171
YR 2023
FD 2023
LK https://uvadoc.uva.es/handle/10324/64910
UL https://uvadoc.uva.es/handle/10324/64910
LA spa
NO Journal of Symbolic Computation, Volume 114, 2023, Pages 1-17,
NO Producción Científica
DS UVaDOC
RD 18-nov-2024