Theorems · Definition · dynamical systems
Function.minimalPeriod
{α : Type u_1} → (α → α) → α → ℕMinimal period of a point x under an endomorphism f. If x is not a periodic point of f,
then minimalPeriod f x = 0.
- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 100 results in Mathlib
- Foundations
- Depth 18 from the axioms, rests on 166 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.findproof · cited by 139
- Function.periodicPtsproof · cited by 33
Cited by110
Results whose statement or proof uses this declaration.
- orderOfproof · cited by 324
- addOrderOfproof · cited by 208
- pow_orderOf_eq_oneproof · cited by 30
- AddAction.periodproof · cited by 26
- MulAction.periodproof · cited by 26
- orderOf_oneproof · cited by 15
- Nat.card_zpowersproof · cited by 13
- Function.periodicOrbitproof · cited by 13
- addOrderOf_nsmul_eq_zeroproof · cited by 11
- Function.isPeriodicPt_minimalPeriodstatement · cited by 11
- Nat.card_zmultiplesproof · cited by 11
- Function.minimalPeriod_pos_of_mem_periodicPtsstatement · cited by 9