Theorems · Theorem · dynamical systems
Function.periodicOrbit_apply_iterate_eq
∀ {α : Type u_1} {f : α → α} {x : α},
x ∈ Function.periodicPts f → ∀ (n : ℕ), Function.periodicOrbit f (f^[n] x) = Function.periodicOrbit f x- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LE.le.trans_ltproof · cited by 795
- Nat.iteratestatement and proof · cited by 740
- Function.minimalPeriodproof · cited by 100
- Cyclestatement · cited by 79
- Function.periodicPtsstatement and proof · cited by 33
- Function.iterate_add_applyproof · cited by 24
- List.length_rotateproof · cited by 19
- Function.periodicOrbitstatement · cited by 13
- List.getElem_rotateproof · cited by 11
- Function.iterate_mod_minimalPeriod_eqproof · cited by 3
- Function.minimalPeriod_apply_iterateproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Function.periodicOrbit_apply_eqproof · cited by 0