Theorems · Theorem · dynamical systems
MulAction.zpow_smul_eq_iff_period_dvd
∀ {α : Type v} {G : Type u} [inst : Group G] [inst_1 : MulAction G α] {j : ℤ} {g : G} {a : α},
g ^ j • a = a ↔ ↑(MulAction.period g a) ∣ j- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- zpow_natCastproof · cited by 271
- zpow_negproof · cited by 198
- MulAction.periodstatement and proof · cited by 26
- inv_smul_eq_iffproof · cited by 16
- MulAction.pow_smul_eq_iff_period_dvdproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- MulAction.zpow_mod_period_smulproof · cited by 3
- MulAction.zpow_smul_eq_iff_minimalPeriod_dvdproof · cited by 1