Theorems · Definition · dynamical systems
MulAction.period
{α : Type v} → {M : Type u} → [inst : Monoid M] → [MulAction M α] → M → α → ℕThe period of a multiplicative action of g on a is the smallest positive n such that
g ^ n • 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.
Cites3
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
- Function.minimalPeriodproof · cited by 100
Cited by26
Results whose statement or proof uses this declaration.
- MulAction.period_eq_minimalPeriodstatement · cited by 6
- MulAction.pow_smul_eq_iff_period_dvdstatement · cited by 5
- MulAction.zpow_mod_period_smulstatement and proof · cited by 3
- MulAction.pow_mod_period_smulstatement and proof · cited by 3
- MulAction.zpow_smul_eq_iff_period_dvdstatement and proof · cited by 2
- MulAction.period_dvd_exponentstatement · cited by 2
- MulAction.period_dvd_orderOfstatement · cited by 2
- MulAction.period_le_of_fixedstatement · cited by 2
- MulAction.pow_period_smulstatement · cited by 2
- MulAction.zpow_smul_eq_iff_minimalPeriod_dvdproof · cited by 1
- MulAction.period_eq_one_iffstatement and proof · cited by 1
- MulAction.period_le_exponentstatement · cited by 1