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Show existence of arc-length parameterized period p'...

  1. Feb 16, 2017 #1
    1. The problem statement, all variables and given/known data

    Let γ : R → Rn be a regular (smooth) closed curve with period p. Show that there exist an orientation preserving diffeomorphism ϕ: R → R, a number p' ∈ R such that ϕ(s + p') = ϕ(s) + p and γ' = γ ◦ ϕ is an arclength parametrized closed curve with period p'

    2. Relevant equations
    Arc-length Parameterized Curve: Length = ||dγ/dt|| = 1
    Orientation preserving: dΦ/dt > 0 for all t


    3. The attempt at a solution
    So essentially this question is asking for the existence of a number p' such that when we reparameterize by arc-length we have a new (arclength parameterized) period. Is this correct? And if so, how should I go about proving the existence of such a number? Thanks so much in advance folks, I'm looking forward to the lively discussion!
     
  2. jcsd
  3. Feb 23, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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