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nlin.CD2024
Robust chaos in
Indranil Ghosh, David J. W. Simpson
We treat -dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions f…
math.DS2024
The two-dimensional border-collision normal form with a zero determinant
David J. W. Simpson
The border-collision normal form is a piecewise-linear family of continuous maps that describe the dynamics near border-collision bifurcations. Most prior studies assume each piece…
nlin.CD2024
The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps
Indranil Ghosh, Robert I. McLachlan, David J. W. Simpson
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attracto…