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92416a2 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | import OAI.Dynamics.EntropyCounterexample.ClockQuotient
namespace OAI
noncomputable section
open Set Function
open scoped ContDiff
namespace Problem340.ClockQuotient
variable {E F : Type*}
theorem periodize_eq_clockPeriodization [TopologicalSpace E] [NormedAddCommGroup F]
{P a b : ℝ} {f : ℝ × E → F} (hP : 0 < P)
(hsupp : ∀ x, f x ≠ 0 → x.1 ∈ Icc a b) :
periodize P f = ClockPeriodization.periodize P f := by
funext x
exact periodize_eq_tsum hP hsupp x
theorem contDiff_periodize [NormedAddCommGroup E] [NormedSpace ℝ E]
[NormedAddCommGroup F] [NormedSpace ℝ F]
{P a b : ℝ} {n : ℕ∞ω} {f : ℝ × E → F} (hP : 0 < P)
(hf : ContDiff ℝ n f) (hsupp : ∀ x, f x ≠ 0 → x.1 ∈ Icc a b) :
ContDiff ℝ n (periodize P f) := by
rw [periodize_eq_clockPeriodization hP hsupp]
exact ClockPeriodization.contDiff_periodize hP hf hsupp
end Problem340.ClockQuotient
end
end OAI
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