We consider functions with isolated critical points on a closed surface. We prove that in a neighborhood of a critical point the function conjugates with Rez k for the some nonnegative integer k. The full topological invariant of such functions is constructed.1991 Mathematics Subject Classification. 57R45, 57R70, 58C27.
To investigate the topological structure of Morse flows with a sink on the 2-sphere we use the planar tree as complete topological invariant of the flow. We give a list of all planar tree with at least 7 edges. We use a list of rooted planar trees.
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