# Metric geometry: geodesics that meet angle 0 in space CAT (0)

Consider two different geodesics $$gamma_1$$ Y $$gamma_2$$ in a cat$$0$$) Space, issued from the same base point.
A trivial example where we have. $$angle ( gamma_1, gamma_2) = 0$$ is when
$$gamma_1 (t) = gamma_2 (t)$$ for $$t$$ smaller than some $$varepsilon> 0$$. In this case, I say that they define the same germ.

My question is, Are there examples of CAT (0) spaces with geodesics that meet angle 0 and each geodetic has no ramifications? ?

The only kind of examples I know of unbranched geodesics that meet at an angle $$0$$ They are constructed in the following way:
consider the following subset of the Euclidean plane, with induced metric length,
$$X = {(x, y); 0 le x le 1, 0 le and le x ^ 2 }$$. It is a CAT (0) space,
the geodesic between $$(0,0)$$ Y $$(0,1)$$ It is the segment and the geodesic between $$(0,0)$$ Y $$(1,1)$$ It is the arch of the parabola. These geodesics are found in $$(0,0)$$ with angle 0 and do not define the same germ.

However, in this space there are branched geodesics, for example.
the geodesic between $$(0,0)$$ Y $$(1, t)$$ for $$t> 0$$ All define the same germ.