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9eeb9c7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | import OAI.Analysis.IrrationalRotation.Model.SawtoothSmoothing
import Mathlib.Topology.Instances.AddCircle.Defs
namespace OAI
noncomputable section
namespace InvariantProjection.Continuity
def circleSmoothSawtooth (δ : ℝ) : AddCircle (1 : ℝ) → ℝ :=
AddCircle.liftIco 1 0 (smoothSawtooth δ)
def circleSmoothedDrop (C a δ : ℝ) (x : AddCircle (1 : ℝ)) : ℝ :=
C * (a + circleSmoothSawtooth δ x - circleSmoothSawtooth δ (x + (a : AddCircle (1 : ℝ))))
def circleSmoothingTransfer (C δ : ℝ) (x : AddCircle (1 : ℝ)) : ℝ :=
C * (circleSmoothSawtooth δ x - (AddCircle.equivIco 1 0 x : ℝ))
end InvariantProjection.Continuity
end
end OAI
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