Please use this identifier to cite or link to this item:
http://hdl.handle.net/11144/3119
Title: | The beta-transformation's companion map for Pisot or Salem numbers and their periodic orbits |
Authors: | Maia, Bruno |
Keywords: | Beta-transformation companion matrix Pisot Salem periodic orbit |
Issue Date: | 2017 |
Publisher: | Taylor & Francis |
Abstract: | The -transformation of the unit interval is de ned by T (x) := x (mod 1). Its eventually periodic points are a subset of [0; 1] intersected with the eld extension Q( ). If > 1 is an algebraic integer of degree d > 1, then Q( ) is a Q-vector space isomorphic to Q d , therefore the intersection of [0; 1] with Q( ) is isomorphic to a domain in Q d . The transformation from this domain which is conjugate to the -transformation is called the companion map, given its connection to the companion matrix of 's minimal polynomial. The companion map and the proposed notation provide a natural setting to reformulate a classic result concerning the set of periodic points of the -transformation for Pisot numbers. It also allows to visualize orbits in a d-dimensional space. Finally, we refer connections with arithmetic codings and symbolic representations of hyperbolic toral automorphisms. |
Peer Reviewed: | yes |
URI: | http://hdl.handle.net/11144/3119 |
metadata.dc.identifier.doi: | 10.1080/14689367.2017.1288701 |
ISSN: | 1468-9367 |
Publisher Version: | http://www.tandfonline.com/doi/abs/10.1080/14689367.2017.1288701 |
Appears in Collections: | DCEE - Artigos/Papers |
Files in This Item:
File | Description | Size | Format | |
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CompanionMap_BrunoMaia.pdf | 327,51 kB | Adobe PDF | View/Open |
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