Theorems · Theorem · dynamical systems
CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux
∀ (f : CircleDeg1Lift) (x : ℕ → ℝ) (C : ℝ),
(∀ (n : ℕ), dist ((f ^ n) 0) (x n) ≤ C) →
Filter.Tendsto (fun n => x (2 ^ n) / 2 ^ n) Filter.atTop (nhds f.translationNumber)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- MulZeroClass.mul_zeroproof · cited by 2,091
- absproof · cited by 1,814
- Dist.diststatement and proof · cited by 1,539
- Filter.Tendsto.compproof · cited by 560
- tendsto_const_nhdsproof · cited by 330
- pow_posproof · cited by 292
- CircleDeg1Liftstatement and proof · cited by 128
Cited by2
Results whose statement or proof uses this declaration.
- CircleDeg1Lift.translationNumber_eq_of_dist_boundedproof · cited by 1
- CircleDeg1Lift.translationNumber_mul_of_commuteproof · cited by 1