Connectedness arguments in linear dynamics
This chapter presents some of the deepest, most beautiful and most useful results from linear dynamics. We obtain Ansari’s theorem that every power of a hypercyclic operator is hypercyclic, the Bourdon–Feldman theorem that every somewhere dense orbit is (everywhere) dense, the Costakis–Peris theorem that every multi-hypercyclic operator is hypercyclic, the León–Müller theorem that any unimodular multiple of a hypercyclic operator is hypercyclic, and the Conejero–Müller–Peris theorem that every operator in a hypercyclic semigroup is hypercyclic.
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