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A short proof of Kontsevich’s cluster conjecture. (English) Zbl 1266.16026
Summary: We give an elementary proof of the Kontsevich conjecture that asserts that the iterations of the noncommutative rational map \(K_r\colon(x,y)\mapsto(xyx^{-1},(1+y^r)x^{-1})\) are given by noncommutative Laurent polynomials.

MSC:
16S38 Rings arising from noncommutative algebraic geometry
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
13F60 Cluster algebras
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