Submission date: 22 March 2024

Abstract:

This article is interested in pullbacks under the logarithmic derivative of algebraic ordinary differential equations. In particular, assuming the solution set of an equation is internal to the constants, we would like to determine when its pullback is itself internal to the constants. To do so, we develop, using model-theoretic Galois theory and differential algebra, a connection between internality of the pullback and the splitting of a short exact sequence of algebraic Galois groups. We then use algebraic group theory to obtain internality and non-internality results.

Mathematics Subject Classification: 03C45, 03C98, 12H05, 12L12

Keywords and phrases:

Full text arXiv 2403.14900: pdf, ps.