Utilize este identificador para referenciar este registo:
http://hdl.handle.net/11144/3119
Título: | The beta-transformation's companion map for Pisot or Salem numbers and their periodic orbits |
Autor: | Maia, Bruno |
Palavras-chave: | Beta-transformation companion matrix Pisot Salem periodic orbit |
Data: | 2017 |
Editora: | Taylor & Francis |
Resumo: | 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. |
Revisão por Pares: | yes |
URI: | http://hdl.handle.net/11144/3119 |
metadata.dc.identifier.doi: | 10.1080/14689367.2017.1288701 |
ISSN: | 1468-9367 |
Versão do editor: | http://www.tandfonline.com/doi/abs/10.1080/14689367.2017.1288701 |
Aparece nas colecções: | DCEE - Artigos/Papers |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
---|---|---|---|---|
CompanionMap_BrunoMaia.pdf | 327,51 kB | Adobe PDF | Ver/Abrir |
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