In a minimal flow, the hitting time is the exponent of the power law, as r goes to zero, for the time needed by orbits to become r-dense. We show that on the so-called Ornithorynque origami, the hitting time of the flow in an irrational slope equals the diophantine type of the slope. We give a general criterion for such equality. In general, for genus at least two, hitting time is strictly bigger than diophantine type.
"A genus 4 origami with minimal hitting time and an intersection property." Illinois J. Math. 65 (3) 579 - 596, September 2021. https://doi.org/10.1215/00192082-9366075