EDB — 1PQ

[1PQ]Prerequisites:[1NX]↺↻,[1PG]↺↻.Let \(𝛾,𝛿\) curves be closed and immersed, but seen as maps defined on \(ℝ\) and \(C^ 1\) and periodic. with periods \(1\).

Let’s see a new relation: you have \(𝛾≈_ f𝛿\) if there is an increasing diffeomorphism \(𝜑:ℝ→ℝ\) such that \(𝜑(t+1)=𝜑(t)+1\) for every \(t∈ℝ\) and for which \(𝛾=𝛿 ◦𝜑\)

Show that this is an equivalence relation.

Compare it with the relation \(≈\).