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Fixed points of local actions of Lie groups on real and complex 2-manifolds. (English) Zbl 1415.37023

Summary: I discuss old and new results on fixed points of local actions by Lie groups \(G\) on real and complex 2-manifolds, and zero sets of Lie algebras of vector fields. Results of E. Lima, J. Plante and C. Bonatti are reviewed.

MSC:

37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
32C05 Real-analytic manifolds, real-analytic spaces
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