论文标题
在多项式双曲线成分上的riemannian度量
A Riemannian metric on polynomial hyperbolic components
论文作者
论文摘要
我们在$ d \ ge 2 $多项式的模量空间中的某些双曲线组件上引入了一个riemannian度量。我们的度量是通过考虑多项式相对于某些平衡状态的度量理论熵来构建的。作为应用程序，我们表明Hausdorff维度功能在此类双曲线组件上没有局部最大值。我们还提供了足够的条件，因为一个不是Hausdorff尺寸函数的关键点。
We introduce a Riemannian metric on certain hyperbolic components in the moduli space of degree $d \ge 2$ polynomials. Our metric is constructed by considering the measure-theoretic entropy of a polynomial with respect to some equilibrium state. As applications, we show that the Hausdorff dimension function has no local maximum on such hyperbolic components. We also give a sufficient condition for a point not being a critical point of the Hausdorff dimension function.
