  Chaotic attractors in the two-dimensional border-collision normal form (a
piecewise-linear map) can persist throughout open regions of parameter space.
Such robust chaos has been established rigorously in some parameter regimes.
Here we provide formal results for robust chaos in the original parameter
regime of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett.
80(14):3049--3052, 1998]. We first construct a trapping region in phase space
to prove the existence of a topological attractor. We then construct an
invariant expanding cone in tangent space to prove that tangent vectors expand
and so no invariant set can have only negative Lyapunov exponents. Under
additional assumptions we also characterise an attractor as the closure of the
unstable manifold of a fixed point.
