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The $$C^1$$ generic diffeomorphism has trivial centralizer. (English) Zbl 1177.37025
Let $$M$$ be a closed manifold and let $$f$$ be its $$C^1$$-diffeomorphism. The paper investigates properties of the centralizer of $$f$$. The centralizer of $$f$$ is called trivial if it is equal to the cyclic group generated by $$f$$. The main result of the paper says that there exists a residual subset of the group of $$C^1$$-diffeomorphisms of $$M$$ consisting of elements with trivial centralizer.

##### MSC:
 37C05 Dynamical systems involving smooth mappings and diffeomorphisms 37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
##### Keywords:
diffeomorphism; centralizer; manifold
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##### References:
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