用多对数估计同时线性化的一个证明

共振条件下全纯芽的同时线性化

Simultaneous linearization of holomorphic germs in presence of resonances

设$f_1, ..., f_m$是$\C^n$的双全纯的$m\ge 2$芽，固定原点，其中$(\d f_1)_O$可对角化，并且对于任何$h=2,..., m$，$f_1$与$f_h$可交换。我们证明了，在对$(\d f_1)_O$的特征值的一定算术条件和对它们的共振的一定限制下，$f_1, ..., f_m$是同时全纯线性化的当且仅当存在一个特定的复流形在$f_1,..., f_m$下不变量.

全纯映射交换芽的全纯线性化

Holomorphic linearization of commuting germs of holomorphic maps

设$f_1, ..., f_h$是固定原点的$\C^n$的双全纯的$h\ge 2$芽.我们调查的形状（正式）同时线性化的给定芽可以有，我们证明，如果$f_1, ..., f_h$交换和他们的线性部分几乎同时Jordanizable然后他们同时正式线性化。接下来，我们引入一个同时Brjuno型条件，并证明，在情况下的线性项的芽是diagonalizable，如果芽交换和我们的Brjuno型条件成立，那么他们是全纯同时线性化。这回答了莫泽提出的一个问题的多维版本。

On Simultaneous Linearization

Given a uniformly quasiregular mapping, there is typically no reason to assume any relationship between linearizers at different repelling periodic points. However, in the current paper we prove that in the case where the uqr map arises as a solution of a Schröder equation then, with some further natural assumptions, if $L$ is a linearizer at one repelling periodic point, then $L\circ T$ is a linearizer at another repelling periodic point, where $T$ is a translation. In this sense we say $L$ simultaneously linearizes $f$. In the plane, an example would be that $e^z$ simultaneously linearizes $…

全纯微分同胚交换芽的同时线性化

Simultaneous linearization of commuting germs of holomorphic diffeomorphisms

设f_1，. f_N是C中固定原点的全纯单同态的交换芽，其无理数与旋转数α_1，.无关，α_N我们将Yoccoz的芽重正化应用到这种设置中，以表明关于旋转数的同时丢番图逼近的Brjuno型条件足以使f_1，.，f_N。这推广了Moser的一个结果。在没有周期轨道的情况下，我们表明，一个较弱的算术条件类似的佩雷斯-马可的情况下，一个单一的胚芽是足够的线性化。我们还获得了下界的共形半径的西格尔磁盘在这两种情况下的算术函数定义的算术条件。

Simultaneous Linearization of Diffeomorphisms of Isotropic Manifolds

Suppose that $M$ is a closed isotropic Riemannian manifold and that $R_1,...,R_m$ generate the isometry group of $M$. Let $f_1,...,f_m$ be smooth perturbations of these isometries. We show that the $f_i$ are simultaneously conjugate to isometries if and only if their associated uniform Bernoulli random walk has all Lyapunov exponents zero. This extends a linearization result of Dolgopyat and Krikorian from $S^n$ to real, complex, and quaternionic projective spaces. In addition, we identify and remedy an oversight in that earlier work.

抛物自映射的同时线性化与中心化 I：零超几何步骤

Simultaneous linearization and centralizers of parabolic self-maps I: zero hyperbolic step

本文研究了抛物自映射的同时线性化与中心化问题，证明了与抛物自映射相容的全纯自映射的条件，并展示了中心化半群的可交换性及单值性性质。