title: Unfolding homoclinic connections formed by corner intersections in piecewise-smooth maps.
abstract: The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, an invariant set can develop a homoclinic connection when its stable manifold intersects a non-differentiable point of its unstable manifold (or vice-versa). This is a codimension-one bifurcation analogous to a homoclinic tangency of a smooth map, referred to here as a homoclinic corner. This paper presents an unfolding of generic homoclinic corners for saddle fixed points of planar piecewise-smooth continuous maps. It is shown that a sequence of border-collision bifurcations limits to a homoclinic corner and that all nearby periodic solutions are unstable.
authors.affiliation: Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand.
authors.forename: D J W
authors.initials: DJ
authors.lastname: Simpson