RT info:eu-repo/semantics/article
T1 Algebraic, rational and Puiseux series solutions of systems of autonomous algebraic ODEs  of dimension one
A1 Cano, José
A1 Falkensteiner, Sebastian
A1 Sendra Pons, Juan Rafael
K1 Algebraic autonomous ordinary differential equation
K1 Formal Puiseux series solution
K1 Algebraic solutions
K1 Rational solutions
K1 Convergent solution
K1 Algebraic space curve
K1 Matemáticas
K1 Mathematics
AB In this paper, we study the algebraic, rational and formal Puiseux series solutions of certain type of systems of autonomous ordinary differential equations. More precisely, we deal with systems which associated algebraic set is of dimension one. We establish a relationship between the solutions of the system and the solutions of an associated first order autonomous ordinary differential equation, that we call the reduced differential equation. Using results on such equations, we prove the convergence of the formal Puiseux series solutions of the system, expanded around a finite point or at infinity, and we present an algorithm to describe them. In addition, we bound the degree of the possible algebraic and rational solutions, and we provide an algorithm to decide their existence and to compute such solutions if they exist. Moreover, if the reduced differential equation is non trivial, for every given point (x0,y0)∈C2, we prove the existence of a convergent Puiseux series solution y(x) of the original system such that y(x0)=y0.
PB Springer
SN 1661-8270
YR 2020
FD 2020-06-05
LK http://hdl.handle.net/10017/49647
UL http://hdl.handle.net/10017/49647
LA eng
NO Agencia Estatal de Investigación
DS MINDS@UW
RD 26-abr-2024