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
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