Introduces weighted-density variants of U-frequent hypercyclicity lying between standard U-frequent and reiterative hypercyclicity, proves that chaos fails to imply any of them, and shows each variant is preserved under finite products.
Ergodic Theory and Dynamical Systems, pages 1–27
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$\mathcal{U}$-Frequent hypercyclicity notions and related weighted densities
Introduces weighted-density variants of U-frequent hypercyclicity lying between standard U-frequent and reiterative hypercyclicity, proves that chaos fails to imply any of them, and shows each variant is preserved under finite products.