Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775435 | Advances in Applied Mathematics | 2017 | 24 Pages |
Abstract
Many sequences of p-adic integers project modulo pα to p-automatic sequences for every αâ¥0. Examples include algebraic sequences of integers, which satisfy this property for every prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. For such a sequence, we construct a profinite automaton that projects modulo pα to the automaton generating the projected sequence. In general, the profinite automaton has infinitely many states. Additionally, we consider the closure of the orbit, under the shift map, of the p-adic integer sequence, defining a shift dynamical system. We describe how this shift is a letter-to-letter coding of a shift generated by a constant-length substitution defined on an uncountable alphabet, and we establish some dynamical properties of these shifts.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Eric Rowland, Reem Yassawi,