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Then

b=y o h is a reparametrization of y.

I want to show:

1) b is a regular closed curve so i'm guessing I needs an expression for the kth derivative

2) there is a regular homotopy between y and b. I have been guided to consider

F:[0,1] x [0,1]->R^n given by $F(u,t)=y(uh(t)+(1-u)t)$.