Theorems · Theorem · dynamical systems
Function.IsFixedPt.map
∀ {α : Type u_1} {β : Type u_2} {fa : α → α} {fb : β → β} {x : α},
Function.IsFixedPt fa x → ∀ {g : α → β}, Function.Semiconj g fa fb → Function.IsFixedPt fb (g x)If g (semi)conjugates fa to fb, then it sends fixed points of fa to fixed points
of fb.
- Defined in
- Mathlib.Dynamics.FixedPoints.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 5 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.
- Function.IsFixedPtstatement and proof · cited by 84
- Function.Semiconjstatement and proof · cited by 82
- Function.Semiconj.eqproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- Function.IsPeriodicPt.mapproof · cited by 2
- Function.Semiconj.mapsTo_fixedPointsproof · cited by 1
- Function.mapsTo_fixedPoints_compproof · cited by 1