Mathematical analysis demonstrates conditions for hypercyclicity and topological mixing in cosine functions, highlighting universal dynamics across complex Banach spaces.
Our first aim in this paper is to give sufficient conditions for the hypercyclicity and topological mixing of a strongly continuous cosine function. We apply these results to study the cosine function associated to translation groups. We also prove that every separable infinite dimensional complex Banach space admits a topologically mixing uniformly continuous cosine family.
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Bonilla et al. (2007) studied this question.
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