Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow
Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow
We extend Mirzakhani's conjugacy between the earthquake and horocycle flows to a bijection, demonstrating conjugacies between these flows on all strata and exhibiting an abundance of new ergodic measures for the earthquake flow.The structure of our map indicates a natural extension of the earthquake flow to an action of the …