Theorems · Theorem · dynamical systems
AddAction.isPeriodicPt_vadd_iff
∀ {α : Type v} {M : Type u} [inst : AddMonoid M] [inst_1 : AddAction M α] {m : M} {a : α} {n : ℕ},
Function.IsPeriodicPt (fun x => m +ᵥ x) n a ↔ n • m +ᵥ a = a- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 4 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- Nat.iterateproof · cited by 740
- Function.IsPeriodicPtstatement and proof · cited by 68
- vadd_iterate_applyproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- AddAction.nsmul_vadd_eq_iff_period_dvdproof · cited by 5
- AddAction.period_le_of_fixedproof · cited by 2
- AddAction.period_pos_of_fixedproof · cited by 1
- AddAction.period_negproof · cited by 0