标题： 多维芽和向量场的显式线性化通过埃卡勒的树展开 显示英文标题

标题： Explicit linearization of multi-dimensional germs and vector fields through Ecalle's tree expansions

摘要： 我们为在固定点处的非共振解析芽微分同胚或在奇点处的非共振解析芽向量场提供了非递归类型的显式公式，在任何复数维度下均适用。 我们得到的形式表达式依赖于埃卡勒的基于树的组合学的一部分，称为“臂模计算”，它们对于离散时间或连续时间的动力系统具有相同的形状。 在布鲁诺的算术条件下，它们使我们能够直接恢复已知的最佳估计，关于解析线性化变量变换的收敛域，以布鲁诺级数的值为基准，包括与问题维度的新精确依赖关系。 显示英文摘要

摘要： We provide explicit formulas of non-recursive type for the linearizing transformations of a non-resonant analytic germ of diffeomorphism at a fixed point or a non-resonant analytic germ of vector field at a singular point, in any complex dimension. The formal expressions we obtain rely on a part of Ecalle's tree-based combinatorics called ``armould calculus" and they have the same shape for dynamical systems with discrete or continuous time. They allow us to recover in a straightforward manner, under Bruno's arithmetical condition, the best known estimates for the domains of convergence of the analytic linearizing changes of variables in terms of the value of the Bruno series, including a new precise dependence with respect to the dimension of the problem.