Nakai, Isao Separatrices for non solvable dynamics on \(\mathbb{C},0\). (English) Zbl 0804.57022 Ann. Inst. Fourier 44, No. 2, 569-599 (1994). We define the separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane \(\mathbb{C}\) and prove their existence for non solvable pseudogroups (Theorem 1). This extends a result by A. A. Shcherbakov [Mosc. Univ. Math. Bull. 37, No. 4, 10- 16 (1982); translation from Vestn. Mosk. Univ., Ser. I 1982, No. 4, 10-15 (1982; Zbl 0517.30009)] accurately. Our method also applies to prove the topological rigidity theorem for generic pseudogroups attributed to Shcherbakov [Tr. Semin. Im. I. G. Petrovskogo 10, 170-196 (1984; Zbl 0568.30010)]. Reviewer: I.Nakai (Sapporo) Cited in 4 ReviewsCited in 39 Documents MSC: 57S99 Topological transformation groups 58H05 Pseudogroups and differentiable groupoids 37-XX Dynamical systems and ergodic theory Keywords:separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane; non solvable pseudogroups; topological rigidity theorem for generic pseudogroups Citations:Zbl 0517.30009; Zbl 0568.30010 PDFBibTeX XMLCite \textit{I. Nakai}, Ann. Inst. Fourier 44, No. 2, 569--599 (1994; Zbl 0804.57022) Full Text: DOI Numdam EuDML References: [1] [1], Fractional iteration near a fixpoint of multiplier 1, J. Australian Math. Soc., 4 (1964), 143-148. · Zbl 0134.05402 [2] [2], Iteration of Rational Functions, Graduate Texts in Math. 132, Springer-Verlag, 1991. · Zbl 0742.30002 [3] [3], Analytic form of differential equations, Transaction Moscow Math. 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