ACAC Seminar Abstract

ACAC Seminar Abstract

ACAC Seminars

ACAC Seminar Abstract

Algebraic differential equations and their rational solutions

Speaker: Franz Winkler
Date, Time: Fri, 15 Feb 2013 14:30

Consider an algebraic ordinary differential equation (AODE), i.e. a polynomial relation between the unknown function and its derivatives. This polynomial defines an algebraic hypersurface. By considering rational parametrizations of this hypersurface, we can decide the rational solvability of the given AODE, and in fact compute the general rational solution. This method depends crucially on curve and surface parametrization and the determination of rational invariant algebraic curves.
For AODEs of order 1 we present a complete algorithm. Further research is directed towards AODEs of higher order, and a classification of AODEs w.r.t. groups of transformations (affine, birational) preserving rational solvability.

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