On solution manifolds of differential systems with discrete state-dependent delays

<p style='text-indent:20px;'>For differential equations with state-dependent delays the associated initial value problem is well-posed, differentiable solution operators, on submanifolds of space <inline-formula><tex-math id="M1">\begin{document}$ C^1_n=C^1([-r,0],\mathbb{R}^n) $\end{document}</tex-math></inline-formula>, under mild smoothness assumptions. We study these <i>solution manifolds</i> and find that for a large class their manifolds are nearly as simple graph over subspace id="M2">\begin{document}$ X_0\subset C^1_n $\end{document}</tex-math></inline-formula> defined by id="M3">\begin{document}$ \phi'(0)=0 $\end{document}</tex-math></inline-formula>. The result supplements recent work finite atlases related to open whether in some cases constructed minimal.</p>