Calculation of cantori for Hamiltonian flows

Area of Science:

• Dynamical Systems and Chaos Theory
• Plasma Physics and Fusion Energy

Background:

• Cantori are invariant sets that form partial transport barriers in chaotic dynamical systems.
• Approximating cantori is crucial for understanding transport phenomena in areas like plasma physics.
• Traditional methods like field line tracing struggle to locate periodic orbits accurately in chaotic regions.

Purpose of the Study:

• To develop a robust and efficient method for approximating cantori in continuous flow dynamics.
• To identify high-order periodic orbits that closely represent cantori.
• To overcome the limitations of existing methods in chaotic environments.

Main Methods:

• Utilized Lagrangian variational methods to determine high-order periodic orbits.
• Focused on constructing minimizing-periodic orbits with extended periodicities.
• Employed a computational approach with linear scaling for cost relative to orbit periodicity.

Main Results:

• Successfully constructed minimizing-periodic orbits with periodicities in the tens of thousands.
• Demonstrated that these orbits closely approximate cantori.
• The developed method shows robustness to chaos and quadratic convergence.

Conclusions:

• Lagrangian variational methods provide an effective means to approximate cantori.
• The technique is computationally efficient and scalable for long periodic orbits.
• This advancement facilitates better understanding of transport barriers in chaotic systems.