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math.DS2026
One-dimensional first return maps for the two-dimensional border-collision normal form with a zero determinant
David J. W. Simpson
The two-dimensional border-collision normal form is a four-parameter family of continuous, piecewise-linear maps. When this form has a zero determinant, all of its nonlinear dynami…
math.DS2026
The stability of boundary equilibria of three-dimensional Filippov systems
David J. W. Simpson
For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equil…