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This paper concerns the two-dimensional border-collision normal form -- afour-parameter family of piecewise-linear maps generalising the Lozi family andrelevant to diverse applications. The normal form was recently shown to exhibita chaotic attractor throughout an open region of parameter space. This wasachieved by constructing a trapping region in phase space and an invariantexpanding cone in tangent space, but only allowed parameter combinations forwhich the normal form is invertible and orientation-preserving. This papergeneralises the construction to include the non-invertible andorientation-reversing cases. This provides a more complete and unified pictureof robust chaos by revealing its presence to be disassociated from the globaltopological properties of the map. We identify a region of parameter space inwhich the map exhibits robust chaos, and show that part of the boundary of thisregion consists of bifurcation points at which the chaotic attractor isdestroyed.

Robust chaos in orientation-reversing and non-invertible two-dimensional piecewise-linear maps