Theorems · Theorem · dynamical systems
MulAction.isPeriodicPt_smul_iff
∀ {α : Type v} {M : Type u} [inst : Monoid M] [inst_1 : MulAction M α] {m : M} {a : α} {n : ℕ},
Function.IsPeriodicPt (fun x => m • x) n a ↔ m ^ n • a = a- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- MulActionstatement and proof · cited by 1,294
- Nat.iterateproof · cited by 740
- Function.IsPeriodicPtstatement and proof · cited by 68
- smul_iterate_applyproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MulAction.pow_smul_eq_iff_period_dvdproof · cited by 5
- MulAction.period_le_of_fixedproof · cited by 2
- MulAction.period_pos_of_fixedproof · cited by 1