1999/10/06 by Marco Abate, Abate, Marco
Mathematics · Physics and Astronomy · #32H02 #32H50 (Primary) #58F23 (Secondary) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.CV #math.DS #msc:32H02 #msc:32H50 #msc:58F23
paper · pdf · doi:10.48550/arxiv.math/9910032
Plain-TeX file, 17 pages
arxiv created 1999/10/06 · openalex publication_date 1999/10/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a canonical procedure for associating to any (germ of) holomorphic self-map f of Cn fixing the origin such that dfO is invertible and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p from M to Cn, a point e in M and a (germ of) holomorphic self-map F of M so that: p restricted to the complement of p-1(O) is a biholomorphism between this complement and Cn minus the origin; p semiconjugates f and F; and e is a fixed point of F such that dFe is diagonalizable. Furthermore, we use this construction to describe the local dynamics of such an f nearby the origin when the only eigenvalue of dfO is 1.