Behavior of distant maximal geodesies in 2-dimensional manifolds
/(0):=0.
For all i e \n(a)]
11
#-\ _ M +/(' ~ 1) tiBi is not a lemon
A
~ l - / ( i - l ) otherwise,
and for all / n(a) + 1
Then
/(0:=/(i-D.
rot(a) = lim sup \f(i) |.
Proo/. Eliminate lemons by using compactly supported regular homotopies.
Remark. The proposition clearly implies the fact that for a semi-regular curve a
one has rot(a) ind(a) ~n(a).
a regular curve
an almost regular curve
1.10. Definition, (i) A semi-regular curve a will be called almost regular if
ind(a) = &(ind(a)).
(ii) An almost regular curve will be called regular if in addition ~n{a) = ind(a).
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