Nondeterministic Chaos, and the Two-fold Singularity in Piecewise Smooth Flows

@article{Colombo2011NondeterministicCA,
title={Nondeterministic Chaos, and the Two-fold Singularity in Piecewise Smooth Flows},
author={Alessandro Colombo and Mike R. Jeffrey},
journal={SIAM J. Applied Dynamical Systems},
year={2011},
volume={10},
pages={423-451}
}

A vector field is piecewise smooth if its value jumps across a hypersurface, and a two-fold singularity is a point where the flow is tangent to the hypersurface from both sides. Two-folds are generic in piecewise smooth systems of three or more dimensions. We derive the local dynamics of all possible two-folds in three dimensions, including nonlinear effects around certain bifurcations, finding that they admit a flow exhibiting chaotic but nondeterministic dynamics. In cases where the flow… CONTINUE READING