Diagonalization of non-diagonalizable discrete holomorphic dynamical systems

Details Diagonalization of non-diagonalizable discrete holomorphic dynamical systems Diagonalization of non-diagonalizable discrete holomorphic dynamical systems

1999-10-06

arxiv.org/abs/math/9910032v1

Mathematics

Complex Variables

Plain-TeX file, 17 pages

Scientific paper

We describe a canonical procedure for associating to any (germ of) holomorphic self-map f of C^n fixing the origin such that df_O is invertible and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p from M to C^n, 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 C^n minus the origin; p semiconjugates f and F; and e is a fixed point of F such that dF_e is diagonalizable. Furthermore, we use this construction to describe the local dynamics of such an f nearby the origin when the only eigenvalue of df_O is 1.

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