Theorems · Theorem · dynamical systems
Function.isPeriodicPt_minimalPeriod
∀ {α : Type u_1} (f : α → α) (x : α), Function.IsPeriodicPt f (Function.minimalPeriod f x) x- Defined in
- Mathlib.Dynamics.PeriodicPts.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.minimalPeriodstatement · cited by 100
- Nat.find_specproof · cited by 74
- Function.IsPeriodicPtstatement and proof · cited by 68
- Function.periodicPtsproof · cited by 33
- Function.isPeriodicPt_zeroproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- pow_orderOf_eq_oneproof · cited by 30
- addOrderOf_nsmul_eq_zeroproof · cited by 11
- Function.isPeriodicPt_iff_minimalPeriod_dvdproof · cited by 6
- Function.minimalPeriod_eq_one_iff_isFixedPtproof · cited by 5
- Function.IsPeriodicPt.minimalPeriod_dvdproof · cited by 4
- Function.Commute.minimalPeriod_of_comp_dvd_lcmproof · cited by 3
- Function.iterate_minimalPeriodproof · cited by 3
- Function.iterate_mod_minimalPeriod_eqproof · cited by 3
- Function.Commute.minimalPeriod_of_comp_eq_mul_of_coprimeproof · cited by 2
- Function.minimalPeriod_apply_iterateproof · cited by 2
- Function.iterate_add_minimalPeriod_eqproof · cited by 0