正则多项式自同构的非阿基米德与混合动力学
Non-archimedean and hybrid dynamics of regular polynomial automorphisms
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中文总结 AI 辅助
本文利用混合空间技术，证明正则多项式自同构解析族在退化时的不变测度弱极限等于非阿基米德域上诱导自同构的不变测度，推广了Hénon映射情形的先前结果。
中文摘要 AI 辅助
本文利用Boucksom--Favre--Jonsson发展的混合空间技术，研究了由单位穿孔圆盘参数化、可能在原点退化的$\mathbb{C}^N$上正则多项式自同构解析族$\{f_t\}_{t\in\mathbb{D}^*}$所关联不变测度的弱极限。对每个$t$，不变测度$\mu_t$由Sibony构造，我们证明$\{\mu_t\}_t$在混合空间上的弱极限由原族诱导的$\mathbb{C}((t))$上正则多项式自同构$f_{\mathbb{C}((t))}^{\operatorname{an}}$的不变测度给出。这是作者先前关于Hénon映射动力学退化族结果的推广。
英文摘要
In this paper, we study the weak limit of the invariant measures attached to an analytic family $\{f_t\}_{t\in\mathbb{D}^*}$ of regular polynomial automorphisms over $\mathbb{C}^N$ parametrized by the unit punctured disk which may degenerate at the origin, by using the techniques called hybrid spaces developed by Boucksom--Favre--Jonsson. For each $t$, the invariant measure $μ_t$ is constructed by Sibony, and we show that the weak limit of $\{μ_t\}_t$ over the hybrid space is given by the invariant measure of the regular polynomial automorphism $f_{\mathbb{C}((t))}^{\operatorname{an}}$ over $\mathbb{C}((t))$ induced from the original family. This is a generalization of the author's previous result for degenerating families of dynamics of Hénon mappings.
发表机构
- NTT Institute for Fundamental Mathematics, NTT Communication Science Laboratories, NTT Inc.（日本电信电话株式会社基础数学研究所、通信科学实验室）
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