The authors characterize the periodic directions of straight-line flow on the Mucube via a genus-one quotient and an infinitely generated subgroup of SL(2,Z), determine its Veech group, and prove density of periodic and ergodic directions.
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Straight-line trajectories on the Mucube
The authors characterize the periodic directions of straight-line flow on the Mucube via a genus-one quotient and an infinitely generated subgroup of SL(2,Z), determine its Veech group, and prove density of periodic and ergodic directions.