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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
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