Unfolding homoclinic connections formed by corner intersections in piecewise-smooth maps.

@article{Simpson2016UnfoldingHC,
  title={Unfolding homoclinic connections formed by corner intersections in piecewise-smooth maps.},
  author={David J. W. Simpson},
  journal={Chaos},
  year={2016},
  volume={26 7},
  pages={
          073105
        }
}
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… 
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