具有任意平稳组合的Henon型映射
Henon-like maps with arbitrary stationary combinatorics
摘要：
我们将\cite{dCML}中引入的重正化算子从倍周期Hénon-like映射推广到具有任意平稳组合的Hénon-like映射.我们表明，在这种情况下，如果地图采取的是\emph{strongly dissipative}的重正化图片也持有。我们研究了无限重正化映射$F$，证明了它们有一个不变的康托尔集$\mathcal{O}$，在该集上$F$对某些$p>1$起着$p$ -adic加法机的作用.然后，我们表明，作为\cite{dCML}的倍周期的情况下，序列的重整化有一个泛值型，但不变的康托尔集$\mathcal{O}$是非刚性的。我们还证明了$\mathcal{O}$不可能具有连续不变的线场。
英文摘要：
We extend the renormalisation operator introduced in \cite{dCML} from period-doubling Hénon-like maps to Hénon-like maps with arbitrary stationary combinatorics. We show the renormalisation picture holds also holds in this case if the maps are taken to be \emph{strongly dissipative}. We study infinitely renormalisable maps $F$ and show they have an invariant Cantor set $\mathcal{O}$ on which $F$ acts like a $p$-adic adding machine for some $p>1$. We then show, as for the period-doubling case in \cite{dCML}, the sequence of renormalisations have a universal form, but the invariant Cantor set $\mathcal{O}$ is non-rigid. We also show $\mathcal{O}$ cannot possess a continuous invariant line field.
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