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math.DS2023
The necessity of the sausage-string structure for mode-locking regions of piecewise-linear maps
David J. W. Simpson
Piecewise-smooth maps are used as discrete-time models of dynamical systems whose evolution is governed by different equations under different conditions (e.g.~switched control sys…
math.DS2023
How to compute multi-dimensional stable and unstable manifolds of piecewise-linear maps
D. J. W. Simpson
For piecewise-linear maps the stable and unstable manifolds of hyperbolic periodic solutions are themselves piecewise-linear. Hence compact subsets of these manifolds can be repres…