Iterated Moiré Maps and Braiding of Chiral Polymer Crystals

In the hexagonal columnar phase of chiral polymers a bias towards cholesteric twist competes with braiding along an average direction. When the chirality is strong, screw dislocations proliferate, leading to either a tilt grain boundary phase or a new ``moir\'e state'' with twisted bond order. In the latter case, polymer trajectories in the plane perpendicular to their average direction are described by iterated moir\'e maps of remarkable complexity.