利用$C^d$ -恒等式扰动的重整化实现任意$d$维动力学
Realizing arbitrary $d$-dimensional dynamics by renormalization of $C^d$-perturbations of identity
摘要：
$C^d$维单位球$\mathbb B^d$的任何$C^d$保守映射$f$都可以通过$C^d$恒等式扰动的重正化迭代来实现：存在$\mathbb B^d$的保守同胚，任意接近$C^d$拓扑中的恒等式，其具有周期圆盘，在该圆盘上，$C^d$坐标改变后的返回动力学恰好是$f$。
英文摘要：
Any $C^d$ conservative map $f$ of the $d$-dimensional unit ball $\mathbb B^d$ can be realized by renormalized iteration of a $C^d$ perturbation of identity: there exists a conservative diffeomorphism of $\mathbb B^d$, arbitrarily close to identity in the $C^d$ topology, that has a periodic disc on which the return dynamics after a $C^d$ change of coordinates is exactly $f$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
