Multifractal analysis of local invariance entropies

We introduce two types of (q, μ)-invariance entropies for topological time-invariant control systems. Through an analysis of level sets of local invariance entropies, we establish relationships between Bowen invariance entropy and (q, μ)-Bowen invariance entropy, as well as between packing invariance entropy and (q, μ)-packing invariance entropy. Moreover, we provide an upper estimate on the multifractal spectrum for local invariance entropies, enhancing the understanding of complexity in control systems.