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Conjecture on necessity of a DC component for chaos with a single AC drive

Prove or disprove the conjecture that the rotor Hamiltonian H(t)=L^2/(2I)+K cos(θ)+2K cos(θ) cos(ω t) (i.e., a pendulum with a single AC drive plus a DC component) exhibits classical chaotic dynamics, whereas the rotor Hamiltonian H(t)=L^2/(2I)+2K cos(θ) cos(ω t) (i.e., the same system without the DC component) does not produce chaos.

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Background

Building on the decomposition of the kicked rotor’s pulse train, the authors propose specific Hamiltonians: with only DC (pendulum, integrable), with only AC (single-frequency drive, expected integrable), and with DC plus one AC component (potentially chaotic). They explicitly formulate a conjecture regarding the necessity of the DC component for chaos in the single-frequency driven case.

Establishing this would clarify the minimal ingredients for chaos in 1.5D driven rotor systems and sharpen the comparison to the HHG simple-man model.

References

Thus, we conjecture that without the DC component, this system will not be chaotic; with the DC component, even with one driving field it could be chaotic.

— Attochaos I: The classically chaotic postcursor of high harmonic generation (2405.05804 - Berkheim et al., 9 May 2024) in Section “Future Work”, Subsection “From simple-man to kicked rotor”