Theorems · Theorem · dynamical systems
Function.iterate_fixed
∀ {α : Type u} {f : α → α} {x : α}, f x = x → ∀ (n : ℕ), f^[n] x = x- Defined in
- Mathlib.Logic.Function.Iterate
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
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.iteratestatement and proof · cited by 740
- Function.iterate_succ_applyproof · cited by 18
Cited by9
Results whose statement or proof uses this declaration.
- iterate_map_zeroproof · cited by 9
- Function.IsFixedPt.iterateproof · cited by 9
- iterate_map_oneproof · cited by 3
- IsPredArchimedean.findAtom_botproof · cited by 2
- AddMonoidHom.preErgodic_of_dense_iUnion_preimage_zeroproof · cited by 1
- ergodic_smul_of_denseRange_powproof · cited by 1
- ergodic_vadd_of_denseRange_nsmulproof · cited by 1
- MonoidHom.preErgodic_of_dense_iUnion_preimage_oneproof · cited by 1
- PerfectClosure.natCast_eq_iffproof · cited by 0