Logic Seminar
Chris Miller
Ohio State University
Expansions of the real field by trajectories of linear vector fields
Abstract: Let $F\colon \mathbb R^n\to \mathbb R^n$ be linear and $\gamma\colon \mathbb R\to \mathbb R^n$
be differentiable such that $\gamma'(t)=F(\gamma(t))$ for all $t\in \mathbb R$. Then the image $
\gamma(\mathbb R)$ is interdefinable over the real field with at least one of: the real exponential function
$e^x$; the complex exponential function $e^z$; or a finite set of functions $t\mapsto t^w\colon (0,\infty)
\to \mathbb C$, where $w\in\mathbb C$. Moreover, which case(s) hold can be semialgebraically
computed from the coefficients of $F$.
Tuesday August 29, 2006 at 4:00 PM in SEO 427