Theorems · Theorem · dynamical systems
MulAction.zpow_smul_eq_iff_minimalPeriod_dvd
∀ {α : Type v} {G : Type u} [inst : Group G] [inst_1 : MulAction G α] {a : G} {b : α} {n : ℤ},
a ^ n • b = b ↔ ↑(Function.minimalPeriod (fun x => a • x) b) ∣ n- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- Function.minimalPeriodstatement · cited by 100
- MulAction.periodproof · cited by 26
- MulAction.period_eq_minimalPeriodproof · cited by 6
- MulAction.zpow_smul_eq_iff_period_dvdproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MulAction.mem_fixedBy_zpowproof · cited by 2