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 28-mar-2024