Theorems · Theorem · dynamical systems
Function.minimalPeriod_apply_iterate
∀ {α : Type u_1} {f : α → α} {x : α},
x ∈ Function.periodicPts f → ∀ (n : ℕ), Function.minimalPeriod f (f^[n] x) = Function.minimalPeriod f x- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Nat.iteratestatement and proof · cited by 740
- LE.le.antisymmproof · cited by 507
- Function.minimalPeriodstatement · cited by 100
- Function.IsPeriodicPtproof · cited by 68
- Function.periodicPtsstatement and proof · cited by 33
- Function.isPeriodicPt_minimalPeriodproof · cited by 11
- Function.minimalPeriod_pos_of_mem_periodicPtsproof · cited by 9
- Function.IsPeriodicPt.minimalPeriod_leproof · cited by 9
- Function.IsPeriodicPt.apply_iterateproof · cited by 4
- Function.isPeriodicPt_of_mem_periodicPts_of_isPeriodicPt_iterateproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Function.minimalPeriod_applyproof · cited by 1
- Function.periodicOrbit_apply_iterate_eqproof · cited by 1