Theorems · Theorem · dynamical systems
Function.isPeriodicPt_of_mem_periodicPts_of_isPeriodicPt_iterate
∀ {α : Type u_1} {f : α → α} {x : α} {m n : ℕ},
x ∈ Function.periodicPts f → Function.IsPeriodicPt f m (f^[n] x) → Function.IsPeriodicPt f m x- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, 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
- one_mulproof · cited by 2,841
- LT.lt.leproof · cited by 2,189
- Nat.iteratestatement and proof · cited by 740
- Function.IsPeriodicPtstatement and proof · cited by 68
- Function.periodicPtsstatement and proof · cited by 33
- Function.iterate_add_applyproof · cited by 24
- Function.IsFixedPt.eqproof · cited by 14
- Function.iterate_mulproof · cited by 7
- Function.IsPeriodicPt.apply_iterateproof · cited by 4
- Function.IsPeriodicPt.iterateproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Function.minimalPeriod_apply_iterateproof · cited by 2
- Function.le_of_lt_minimalPeriod_of_iterate_eqproof · cited by 1