Differential equations over polynomially bounded o-minimal structures

We investigate the asymptotic behavior at +∞+\infty of non-oscillatory solutions to differential equations y′=G(t,y),t>ay’=G(t,y), t>a, where G:R1+l→RlG\colon \mathbb {R}^{1+l}\to \mathbb {R}^l is definable in a polynomially bounded o-minimal structure. In particular, we show that the Pfaffian closure of a polynomially bounded o-minimal structure on the real field is levelled.