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Arnold conjecture for surface homeomorphisms. (English) Zbl 0974.37040
It is known that, in dimension two, the Arnold conjecture concerns the fixed points of area preserving diffeomorphism isotopic to the identity with vanishing mean rotation vector. It was solved by many authors using variational arguments. Since Arnold formulated the conjecture within a topological framework it would be natural to answer his conjecture on a geometrical level. This was carried out by Franks for $$C^1$$ diffeomorphisms in his celebrated paper. The main goal of this note is to remark that, with some modifications, Franks’ argument is applicable even for homeomorphisms of closed and oriented surfaces.

MSC:
 37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010) 37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics
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