Diagonalization of non-diagonalizable discrete holomorphic dynamical systems
复变函数
2007-05-23 v1 动力系统
摘要
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.
引用
@article{arxiv.math/9910032,
title = {Diagonalization of non-diagonalizable discrete holomorphic dynamical systems},
author = {Marco Abate},
journal= {arXiv preprint arXiv:math/9910032},
year = {2007}
}
备注
Plain-TeX file, 17 pages