The Arithmetic of Realizable Sequences
نویسنده
چکیده
In this thesis we consider sequences of non-negative integers which arise from counting the periodic points of a map T : X → X, where X is a non-empty set. Some of the main results obtained are concerned with the counting of the periodic points of an endomorphism of a group, in particular when the group is locally nilpotent, for which class of groups a local-global property is established. The ideas developed are applied to some classical sequences, including the Bernoulli and Euler numbers, which are shown to have certain ‘dynamical’ properties. We also consider the Lehmer-Pierce construction for sequences of integers, looking at possible generalizations and their associated measures.
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