Upper Estimates on the Higher-dimensional Multifractal Spectrum of Local Entropy

摘要

We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the higher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractal spetrum of entropies.