论文标题
旋转类的熵光谱
Entropy spectrum of rotation classes
论文作者
论文摘要
在本说明中，我们研究了有限的许多连续电势的旋转类别的熵谱$φ_1，\ dots，φ_m：x \ to \ mathbb {r} $，相对于基本的动态系统$ f：x \ x $ x $的不变度度量。我们显示了大量的动态系统和电势，这些熵光谱在达到零和最大值之间的每个值都可以达到最大。我们还提供了暗示着沿着斜熵光谱的最大性的标准。对于$ m $很大，我们的结果可以解释为在动态环境中经典Riesz代表定理的免费结果。
In this note we study the entropy spectrum of rotation classes for collections of finitely many continuous potentials $φ_1,\dots,φ_m:X\to \mathbb{R}$ with respect to the set of invariant measures of an underlying dynamical system $f:X\to X$. We show for large classes of dynamical systems and potentials that these entropy spectra are maximal in the sense that every value between zero and the maximum is attained. We also provide criteria that imply the maximality of the ergodic entropy spectra. For $m$ being large, our results can be interpreted as a complimentary result to the classical Riesz representation theorem in the dynamical context.
