Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems (Q428768)

From the abstract: ``This article extends results contained in [the authors, J. Differ. Equations 231, No. 2, 633--655 (2006; Zbl 1116.34008)] and [\textit{J. Llibre, P. R. da Silva} and \textit{M. A. Teixeira}, J. Dyn. Differ. Equations 19, No. 2, 309--331 (2007; Zbl 1127.34003); Bull. Belg. Math. Soc. - Simon Stevin 15, No. 5, 851--869 (2008; Zbl 1166.34001)] concerning the dynamics of non-smooth systems. In those papers a piecewise \(C^k\) discontinuous vector field \(Z\) on \(\mathbb{R}^n\) is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets.''