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Theorems · Definition · dynamical systems

Flow.reverse

{τ : Type u_1} →
  {α : Type u_2} →
    [inst : TopologicalSpace τ] →
      [inst_1 : TopologicalSpace α] → [inst_2 : SubtractionCommMonoid τ] → [ContinuousNeg τ] → Flow τ α → Flow τ α

The time-reversal of a flow ϕ by a (commutative, additive) group is defined ϕ.reverse t x = ϕ (-t) x.

Defined in
Mathlib.Dynamics.Flow
Cited by
1 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceSubtractionCommMonoidContinuousNeg
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Flow.reverse_apply · cited by 0Flow.reverse_applyTopologicalSpace · cited by 24529TopologicalSpaceContinuousNeg · cited by 119ContinuousNegSubtractionCommMonoid · cited by 79SubtractionCommMonoidFlow · cited by 46FlowFlow.toFun · cited by 34Flow.toFunFlow.reverseCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.