Calculation of cantori for Hamiltonian flows

Cantori are the invariant sets remaining after the destruction of KAM surfaces and create partial barriers to transport in chaotic regions. Cantori may be approximated by high-order periodic orbits; however, field line tracing methods for locating periodic orbits perform poorly in chaotic regions. To approximate cantori for continuous flow dynamics, high-order periodic orbits are determined by Lagrangian variational methods. The method is robust to chaos, converges quadratically, and the computational cost scales linearly with the periodicity length of the orbit. Minimizing-periodic orbits with periodicities in the tens of thousands, that closely approximate cantori, have been constructed.