Analytic plane sets are locally stars: a dynamically based proof

In 1971, Dennis Sullivan discovered an important obstruction for a topological space to be the set of zeros of a two-variable real analytic function: up to some trivial cases, it must be locally a topological star with evenly many branches.

The property is a very useful tool when dealing with topological dynamics of analytic flows on real surfaces. However, all the proofs of Sullivan’s theorem I am aware of require advanced tools of algebraic topology, and hence are hard to follow for the non-specifically trained reader.

The aim of this talk is to try to justify why the result is important in the field of topological dynamics and to present a proof using only elementary techniques from this field.