Polynomial slow-fast systems on the Poincaré-Lyapunov sphere

The main goal of this paper is to study compactifications of polynomial slow-fast systems. More precisely, the aim is to give conditions in order to guarantee normal hyperbolicity at infinity of the Poincar & eacute;-Lyapunov sphere for slow-fast systems defined in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>{n}$$\end{document}. For the planar case, we prove a global version of the Fenichel Theorem, which assures the persistence of invariant manifolds in the whole Poincar & eacute;-Lyapunov disk. We also discuss the occurrence of non normally hyperbolic points at infinity, namely: fold, transcritical and pitchfork singularities.