Theorems · Theorem · dynamical systems
Function.iterate_mod_minimalPeriod_eq
∀ {α : Type u_1} {f : α → α} {x : α} {n : ℕ}, f^[n % Function.minimalPeriod f x] x = f^[n] x- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 3 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.iteratestatement · cited by 740
- Function.minimalPeriodstatement · cited by 100
- Function.isPeriodicPt_minimalPeriodproof · cited by 11
- Function.IsPeriodicPt.iterate_mod_applyproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Function.periodicOrbit_apply_iterate_eqproof · cited by 1
- Function.mem_periodicOrbit_iffproof · cited by 1
- Function.periodicOrbit_chain'proof · cited by 0