• DOI:10.1063/5.0079807
• Corpus ID: 244709211

Robust Devaney chaos in the two-dimensional border-collision normal form.

@article{Ghosh2022RobustDC,
  title={Robust Devaney chaos in the two-dimensional border-collision normal form.},
  author={Indranil Ghosh and David J. W. Simpson},
  journal={Chaos},
  year={2022},
  volume={32 4},
  pages={
          043120
        }
}

• I. Ghosh, D. Simpson
• Published 25 November 2021
• Mathematics
• Chaos

The collection of all non-degenerate, continuous, two-piece, piecewise-linear maps on R2 can be reduced to a four-parameter family known as the two-dimensional border-collision normal form. We prove that throughout an open region of parameter space, this family has an attractor satisfying Devaney's definition of chaos. This strengthens the existing results on the robustness of chaos in piecewise-linear maps. We further show that the stable manifold of a saddle fixed point, despite being a one-dimensional object, densely fills an open region containing the attractor. Finally, we identify a heteroclinic bifurcation, not described previously, at which the attractor undergoes a crisis and may be destroyed.