交叉口的局部动力学。Arnold定理的再认识
Local dynamics of intersections: V. I. Arnold's theorem revisited
摘要：
V. I. Arnold在1991年证明了（1993年发表）：当一个解析子簇的芽被自映射的迭代所拖动时，在一个全纯可逆自映射的不动点上的两个芽之间的交重数保持有界。证明是基于Skolem-Mahler-Lech定理在递归序列的零点。我们给出了一个不同的证明，基于Noetherianity的某些代数，它允许推广阿诺德定理的局部行动的任意的非线性生成的交换群，无论是离散和无穷小的发电机。简单的例子表明，对于非交换群，类似的断言失败了。
英文摘要：
V. I. Arnold proved in 1991 (published in 1993) that the intersection multiplicity between two germs of analytic subvarieties at a fixed point of a holomorphic invertible self-map remains bounded when one of the germs is dragged by iterations of the self map. The proof is based on the Skolem-Mahler-Lech theorem on zeros in recurrent sequences. We give a different proof, based on the Noetherianity of certain algebras, which allows to generalize the Arnold's theorem for local actions of arbitrary finitely generated commutative groups, both with discrete and infinitesimal generators. Simple examples show that for non-commutative groups the analogous assertion fails.
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