Theorems · Definition · dynamical systems
CircleDeg1Lift.translationNumber
CircleDeg1Lift → ℝ
The translation number of a CircleDeg1Lift, $τ(f)=\lim_{n→∞}\frac{f^n(x)-x}{n}$. We use
an auxiliary sequence \frac{f^{2^n}(0)}{2^n} to define τ(f) because some proofs are simpler
this way.
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 114 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.
- Realstatement · cited by 25,697
- Filter.atTopproof · cited by 2,405
- CircleDeg1Liftstatement and proof · cited by 128
- Filter.limUnderproof · cited by 47
- CircleDeg1Lift.transnumAuxSeqproof · cited by 6
Cited by48
Results whose statement or proof uses this declaration.
- CircleDeg1Lift.translationNumber_le_of_le_add_intstatement · cited by 4
- CircleDeg1Lift.translationNumber_powstatement · cited by 4
- CircleDeg1Lift.le_translationNumber_of_add_int_lestatement · cited by 4
- CircleDeg1Lift.tendsto_translationNumber_auxstatement · cited by 3
- CircleDeg1Lift.translationNumber_monostatement · cited by 2
- CircleDeg1Lift.translationNumber_of_eq_add_intstatement · cited by 2
- CircleDeg1Lift.translationNumber_translatestatement · cited by 2
- CircleDeg1Lift.translationNumber_units_invstatement and proof · cited by 2
- CircleDeg1Lift.map_lt_of_translationNumber_lt_intstatement and proof · cited by 2
- CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_auxstatement · cited by 2
- CircleDeg1Lift.tendsto_translation_number'statement and proof · cited by 2
- CircleDeg1Lift.tendsto_translation_number₀statement and proof · cited by 2