OAI/NumberTheory/DukePrimeDegree/Dynamics/RootFlowGeneric.lean
2 declarations, 0 contain sorry, 0 declared as axioms
Generic sets for the actual root flow
The action used here is the actual right transvection action on the integer-lattice quotient. Its invariant probability has an ergodic decomposition for the entire real flow. On each such ergodic component, the uniform generic-set theorem uses no chosen-time ergodicity premise. The further homogeneous-support conclusion is not asserted here.
- theorem
OAI.DukePrimeDegree.root_flow_ergodic_decompositionline 24 - theorem
OAI.DukePrimeDegree.exists_uniform_root_flow_generic_setline 40Source documentation
Uniform generic sets on an actual root-flow ergodic component.
theorem exists_uniform_root_flow_generic_set {n : ℕ} {i j : Fin n} (hij : i ≠ j) (ν : Measure (X n)) [IsProbabilityMeasure ν] (herg : let := rootTranslationAction hij …