Theorems · Theorem · global analysis

IsMIntegralCurve.periodic_of_eq

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {H : Type u_2} [inst_2 : TopologicalSpace H]
  {I : ModelWithCorners ℝ E H} {M : Type u_3} [inst_3 : TopologicalSpace M] [inst_4 : ChartedSpace H M]
  [inst_5 : IsManifold I 1 M] {γ : ℝ → M} {v : (x : M) → TangentSpace I x} [T2Space M] {a b : ℝ}
  [BoundarylessManifold I M],
  IsMIntegralCurve γ v → (ContMDiff I I.tangent 1 fun x => ⟨x, v x⟩) → γ a = γ b → Function.Periodic γ (a - b)

For a global integral curve γ, if it crosses itself at a b : ℝ, then it is periodic with period a - b.

Defined in

Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique

Cited by

1 results in Mathlib

Foundations

Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifoldT2SpaceBoundarylessManifold