Branched-flow regime vs KAM stickiness influence (conjecture)

Establish whether, in two-dimensional periodic Hamiltonian potentials that exhibit branched flow, the branched-flow regime ends before the stickiness of Kolmogorov–Arnold–Moser (KAM) islands significantly influences the dynamics, thereby testing the conjecture that KAM-induced stickiness does not affect branch decay within the branched-flow time window.

Background

Branch decay in random potentials is known to be exponential, but in periodic Hamiltonian systems, long-time transport can exhibit algebraic behavior due to stickiness near KAM islands and cantori. The paper discusses prior results suggesting algebraic diffusion scaling and compares them to numerical simulations of branched flow in periodic potentials.

The authors report that their simulations do not show clear signs of algebraic branch decay within the time scales of branched flow and explicitly conjecture that the branched-flow regime occurs before stickiness becomes dynamically relevant. This conjecture targets the interplay between short-time branch formation/decay and long-time sticky transport.