Centralizers and normalizers of local analytic and formal vector fields

关于里程计和Toeplitz子移位的中心化子群与正规化子群

On the centralizer and normalizer groups of odometers and Toeplitz subshifts

本文研究剩余有限群下里程计及Toeplitz子移位的自同构与正规化子群，证明对$\mathbb{Z}^d$轨道等价正规化子可通约，对其他幂零群不成立，并构造低复杂度例子展示中心化子受限而正规化子可极大的灵活性。

A p-adic approach to local analytic dynamics: analytic flows and analytic maps tangent to the identity

In this note, we will consider the question of local equivalence of analytic functions which fix the origin and are tangent to the identity, as well as the question of flows of analytic vector fields. All mappings and equivalences are considered in the non-archimedean context e.g. all norms can be considered $p$-adic norms. We show that any two mappings $f$ and $g$ which are formally equivalent are also analytically equivalent, and we show that analytic vector fields generate analytic flows. We consider the related questions of roots and centralizers for analytic mappings. In this setting, any…

Normalisation holomorphe d'algèbres de type Cartan de champs de vecteurs holomorphes singuliers

We consider a commutative family of holomorphic vector fields in an neighbourhood of a common singular point, say $0\in \Bbb C^n$. Let $\lie g$ be a commutative complex Lie algebra of dimension $l$. Let $λ_1,...,λ_n\in \lie g^*$ and let us set $S(g)=\sum_{i=1}^nλ_i(g)x_i\frac{\partial}{\partial x_i}$. We assume that this Lie morphism is {\bf diophantine} in the sense that a diophantine condition $(ω(S))$ is satisfied. Let $X_1$ be a holomorphic vector field in a neighbourhood of $0\in \Bbb C^n$. We assume that its linear part $s$ is regular relatively to $S$, that is belongs to $S(\lie g)$ and…