Theorems · Theorem · dynamical systems
CircleDeg1Lift.translationNumber_of_eq_add_int
∀ (f : CircleDeg1Lift) {x : ℝ} {m : ℤ}, f x = x + ↑m → f.translationNumber = ↑mIf f x - x is an integer number m for some point x, then τ f = m.
On the circle this means that a map with a fixed point has rotation number zero.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- le_antisymmproof · cited by 2,068
- le_of_eqproof · cited by 366
- CircleDeg1Liftstatement and proof · cited by 128
- CircleDeg1Lift.translationNumberstatement · cited by 48
- CircleDeg1Lift.translationNumber_le_of_le_add_intproof · cited by 4
- CircleDeg1Lift.le_translationNumber_of_add_int_leproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- CircleDeg1Lift.translationNumber_eq_int_iffproof · cited by 1
- CircleDeg1Lift.translationNumber_of_map_pow_eq_add_intproof · cited by 0