论文标题
多项式的非构造的Lyapunov指数
Nonarchimedean Lyapunov exponents of polynomials
论文作者
论文摘要
令$ k $为具有特征性$ 0 $的代数封闭和完整的非架构字段，而在k [z] $中$ f \ f \ in k [z] $为$ d \ ge 2 $的多项式。我们研究了$ f $ f $ f $ $ f $的lyapunov指数$ l（f，μ）$ f $，相对于Berkovich Julia套装$ f $的$ f $ invariant和ergodic radon概率量$μ$，下Lyapunov offention $ f $和下Lyapunov expents $ l_f^{ - }（f（c）$ f $ f（c）$ f $ a prigith $ f（c）$ f（c）$ f（c）$ f（c）。在一个集成性假设下，我们显示$ l（f，μ）$仅取决于$ d $和$ k $。特别是，如果$ f $是驯服的，并且没有流浪的非经典朱莉亚积分，则$ l（f，μ）$是无负的；此外，如果另外$ f $具有唯一的朱莉娅关键点$ C_0 $，我们显示$ l_f^{ - }（f（c_0））$也是无负的。
Let $K$ be an algebraically closed and complete nonarchimedean field with characteristic $0$ and let $f\in K[z]$ be a polynomial of degree $d\ge 2$. We study the Lyapunov exponent $L(f,μ)$ of $f$ with respect to an $f$-invariant and ergodic Radon probability measure $μ$ on the Berkovich Julia set of $f$ and the lower Lyapunov exponent $L_f^{-}(f(c))$ of $f$ at a critical value $f(c)$. Under an integrability assumption, we show $L(f,μ)$ has a lower bound only depending on $d$ and $K$. In particular, if $f$ is tame and has no wandering nonclassical Julia points, then $L(f,μ)$ is nonnegative; moreover, if in addition $f$ possesses a unique Julia critical point $c_0$, we show $L_f^{-}(f(c_0))$ is also nonnegative.
