Variational properties of multifractal spectra
Variational properties of multifractal spectra
复制标题
多重分形谱的变分性质
DOI：
10.1088/0951-7715/14/2/305
复制
发表时间：
2001
期刊：
影响因子：
1.7
通讯作者：
L. Barreira
中科院分区：
文献类型：
--
作者：
L. Barreira
对于双曲型超同态，我们描述了局部极大双曲集上的平衡测度的维数谱在测度或动力系统扰动时的变分性质。我们还获得了显式表达式的维数谱和相关的勒让德变换的一阶导数。这使我们能够建立一个本地版本的多重分形刚性，即一个“多重分形”分类的动力系统的基础上，他们的多重分形谱。
For hyperbolic diffeomorphisms, we describe the variational properties of the dimension spectrum of equilibrium measures on locally maximal hyperbolic sets, when the measure or the dynamical system are perturbed. We also obtain explicit expressions for the first derivative of the dimension spectra and the associated Legendre transforms. This allows us to establish a local version of multifractal rigidity, i.e. of a `multifractal' classification of dynamical systems based on their multifractal spectra.