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math.DS2021
Inclusion of higher-order terms in the border-collision normal form: persistence of chaos and applications to power converters
David J. W. Simpson, Paul A. Glendinning
The dynamics near a border-collision bifurcation are approximated to leading order by a continuous, piecewise-linear map. The purpose of this paper is to consider the higher-order…
math.DS2021★ 1 cited
Chaos in the border-collision normal form: A computer-assisted proof using induced maps and invariant expanding cones
P. A. Glendinning, D. J. W. Simpson
In some maps the existence of an attractor with a positive Lyapunov exponent can be proved by constructing a trapping region in phase space and an invariant expanding cone in tange…