Multifractal analysis uncovers relationships in local invariance entropies, implying improved understanding of control systems complexity.
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.
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Hu et al. (2026) studied this question.
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