Theorems · Theorem · dynamical systems
Function.minimalPeriod_eq_one_iff_isFixedPt
∀ {α : Type u_1} {f : α → α} {x : α}, Function.minimalPeriod f x = 1 ↔ Function.IsFixedPt f x- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LE.le.antisymmproof · cited by 507
- Function.minimalPeriodstatement and proof · cited by 100
- Function.IsFixedPtstatement and proof · cited by 84
- Function.IsPeriodicPtproof · cited by 68
- Function.iterate_oneproof · cited by 34
- Function.isPeriodicPt_minimalPeriodproof · cited by 11
- Function.IsPeriodicPt.minimalPeriod_leproof · cited by 9
- Function.IsPeriodicPt.minimalPeriod_posproof · cited by 6
- Function.IsPeriodicPt.isFixedPtproof · cited by 3
- Function.IsFixedPt.isPeriodicPtproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- orderOf_eq_one_iffproof · cited by 12
- AddMonoid.addOrderOf_eq_one_iffproof · cited by 6
- Function.minimalPeriod_eq_prime_iffproof · cited by 3
- AddAction.minimalPeriod_eq_one_iff_fixedByproof · cited by 1
- MulAction.minimalPeriod_eq_one_iff_fixedByproof · cited by 1