Solutions of definable ODEs with regular separation and dichotomy interlacement versus Hardy

Olivier Le Gal, Mickaël Matusinski, Fernando Sanz Sánchez

We introduce a notion of regular separation for solutions of systems of ODEs $y^{\prime }=F(x,y)$, where F is definable in a polynomially bounded o-minimal structure and $y=(y_1,y_2)$. Gi…