Theorems · Theorem · dynamical systems
Function.IsFixedPt.iterate
∀ {α : Type u_1} {f : α → α} {x : α}, Function.IsFixedPt f x → ∀ (n : ℕ), Function.IsFixedPt f^[n] xIf x is a fixed point of f, then it is a fixed point of f^[n].
- Defined in
- Mathlib.Dynamics.FixedPoints.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.iteratestatement · cited by 740
- Function.IsFixedPtstatement and proof · cited by 84
- Function.iterate_fixedproof · cited by 9
Cited by9
Results whose statement or proof uses this declaration.
- Function.IsPeriodicPt.mul_constproof · cited by 6
- Function.IsFixedPt.preimage_iterateproof · cited by 4
- Function.IsFixedPt.image_iterateproof · cited by 2
- Function.IsFixedPt.isPeriodicPtproof · cited by 2
- Equiv.Perm.IsCycleOn.pow_apply_eqproof · cited by 2
- Function.IsFixedPt.perm_powproof · cited by 2
- Function.IsFixedPt.birkhoffSum_eqproof · cited by 1
- Function.IsPeriodicPt.iterateproof · cited by 1
- ODE.FunSpace.exists_forall_closedBall_funSpace_dist_le_mulproof · cited by 1