OAI/NumberTheory/DukePrimeDegree/Dynamics/ReverseRootFlow.lean

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4 declarations, 0 contain sorry, 0 declared as axioms

The reverse root flow used by a right-action shearing pair

For points separated on the right by g, sampling both at U(-t) gives relative displacement U(t) g U(-t). This action has exactly the same invariant sets as the original root flow, so its ergodicity follows from full real-root ergodicity, without selecting a discrete time.

  1. def OAI.DukePrimeDegree.reverseRootTranslationAction line 20
  2. lemma OAI.DukePrimeDegree.reverseRootTranslationAction_continuous line 34
  3. theorem OAI.DukePrimeDegree.reverseRootTranslationAction_ergodic line 46
  4. lemma OAI.DukePrimeDegree.reverse_root_pair_displacement line 72