Theorems · Theorem · dynamical systems
Function.isPeriodicPt_iff_minimalPeriod_dvd
∀ {α : Type u_1} {f : α → α} {x : α} {n : ℕ}, Function.IsPeriodicPt f n x ↔ Function.minimalPeriod f x ∣ n- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, 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.
- Function.minimalPeriodstatement and proof · cited by 100
- Function.IsPeriodicPtstatement · cited by 68
- Function.isPeriodicPt_minimalPeriodproof · cited by 11
- Function.IsPeriodicPt.minimalPeriod_dvdproof · cited by 4
- Function.IsPeriodicPt.trans_dvdproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- AddAction.nsmul_vadd_eq_iff_period_dvdproof · cited by 5
- MulAction.pow_smul_eq_iff_period_dvdproof · cited by 5
- Function.Commute.minimalPeriod_of_comp_dvd_lcmproof · cited by 3
- Function.minimalPeriod_eq_prime_iffproof · cited by 3
- Function.minimalPeriod_eq_prime_powproof · cited by 2
- Function.isPeriodicPt_factorial_card_of_mem_periodicPtsproof · cited by 1