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- W2600692871 abstract "It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fr'echet spaces. We show the existence of frequently hypercyclic homogeneous polynomials on $H(mathbb C)$. We prove that the homogeneous polynomial on $H(mathbb C)$ defined as the product of a translation operator and the evaluation at 0 is topologically mixing, frequently hypercyclic and chaotic. We prove, in contrast, that the product of the differentiation operator and the evaluation at 0, and some other related homogeneous polynomials fail to be hypercyclic." @default.
- W2600692871 created "2017-04-07" @default.
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- W2600692871 date "2017-03-14" @default.
- W2600692871 modified "2023-09-27" @default.
- W2600692871 title "Hypercyclic homogeneous polynomials on $H(mathbb C)$" @default.
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