Theorems · Definition · dynamical systems
AddAction.period
{α : Type v} → {M : Type u} → [inst : AddMonoid M] → [AddAction M α] → M → α → ℕThe period of an additive action of g on a is the smallest positive n
such that (n • g) +ᵥ a = a, or 0 if such an n does not exist.
- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.hVAddproof · cited by 1,820
- AddActionstatement and proof · cited by 820
- Function.minimalPeriodproof · cited by 100
Cited by26
Results whose statement or proof uses this declaration.
- AddAction.period_eq_minimalPeriodstatement · cited by 6
- AddAction.nsmul_vadd_eq_iff_period_dvdstatement · cited by 5
- AddAction.nsmul_mod_period_vaddstatement and proof · cited by 3
- AddAction.zsmul_mod_period_vaddstatement and proof · cited by 3
- AddAction.period_dvd_addOrderOfstatement · cited by 2
- AddAction.period_dvd_exponentstatement · cited by 2
- AddAction.period_le_of_fixedstatement · cited by 2
- AddAction.nsmul_period_vaddstatement · cited by 2
- AddAction.zsmul_vadd_eq_iff_period_dvdstatement and proof · cited by 2
- AddAction.period_eq_zero_iffstatement and proof · cited by 1
- AddAction.period_le_exponentstatement · cited by 1
- AddAction.period_pos_of_fixedstatement · cited by 1