| Title |
Rational matrix digit systems / |
| Authors |
Jankauskas, Jonas ; Thuswaldner, Jörg M |
| DOI |
10.1080/03081087.2022.2067813 |
| Full Text |
|
| Is Part of |
Linear & multilinear algebra.. Abingdon : Taylor and Francis Ltd.. 2023, vol. 71, iss. 10, p. 1606-1639.. ISSN 0308-1087. eISSN 1563-5139 |
| Keywords [eng] |
Digit expansion ; matrix number systems ; dynamical systems ; convex digit sets ; lattices |
| Abstract [eng] |
Let A be a (Formula presented.) matrix with rational entries which has no eigenvalue (Formula presented.) of absolute value (Formula presented.) and let (Formula presented.) be the smallest nontrivial A-invariant (Formula presented.) -module. We lay down a theoretical framework for the construction of digit systems (Formula presented.), where (Formula presented.) finite, that admit finite expansions of the form (Formula presented.) for every element (Formula presented.). We put special emphasis on the explicit computation of small digit sets (Formula presented.) that admit this property for a given matrix A, using techniques from matrix theory, convex geometry, and the Smith Normal Form. Moreover, we provide a new proof of general results on this finiteness property and recover analogous finiteness results for digit systems in number fields a unified way. |
| Published |
Abingdon : Taylor and Francis Ltd |
| Type |
Journal article |
| Language |
English |
| Publication date |
2023 |
| CC license |
|
