Chaotic Dynamics in Circular-Control Fuller Systems

Investigate and rigorously establish whether trajectories of the Fuller (or modified circular-control) optimal control system exhibit chaotic behavior for certain parameter values, and characterize the parameter regimes and dynamical features (e.g., invariant sets, sensitivity to initial conditions) that yield chaos.

Background

The book studies a circular-control variant of the Reinhardt problem as a symmetry-enhanced toy model and analyzes the associated Fuller system. Numerical experiments suggest complex dynamics, and the authors explicitly conjecture the existence of chaos for certain parameter values.

They direct readers to an appendix of research problems for related investigations, highlighting the open status of rigorous chaotic behavior in this setting.