Hall, Toby
(2014)
'Symbol ratio minimax sequences in the lexicographic order'.
Ergodic Theory and Dynamical Systems.
(In Press)
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Abstract
Consider the space of sequences of k letters ordered lexicographically. We study the set M(α) of all maximal sequences for which the asymptotic proportions α of the letters are prescribed, where a sequence is said to be maximal if it is at least as great as all of its tails. The infimum of M(α) is called the α-infimax sequence, or the α-minimax sequence if the infimum is a minimum. We give an algorithm which yields all infimax sequences, and show that the infimax is not a minimax if and only if it is the α-infimax for every α in a simplex of dimension 1 or greater. These results have applications to the theory of rotation sets of beta-shifts and torus homeomorphisms.
| Item Type: | Article |
|---|---|
| Additional Information: | ## TULIP Type: Articles/Papers (Journal) ## |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 29 Jul 2015 11:14 |
| Last Modified: | 17 Dec 2022 01:06 |
| DOI: | 10.1017/etds.2014.44 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/2018299 |
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- 'Symbol ratio minimax sequences in the lexicographic order'. (deposited 29 Jul 2015 11:14) [Currently Displayed]
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