On the Pisot Substitution Conjecture View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2015

AUTHORS

S. Akiyama , M. Barge , V. Berthé , J.-Y. Lee , A. Siegel

ABSTRACT

Our goal is to present a unified and reasonably complete account of the various conjectures, known as Pisot conjectures, that assert that certain dynamical systems arising from substitutions should have pure discrete dynamical spectrum. We describe the various contexts (symbolic, geometrical, arithmetical) in which substitution dynamical systems arise and review the relevant properties of these systems. The Pisot Substitution Conjecture is stated in each context and the relationships between these statements, and with several related conjectures, are discussed. We survey the special cases in which the Pisot Substitution Conjecture has been verified and present algorithmic procedures for checking pure discrete spectrum. We conclude with a discussion of possible extensions to higher dimensions. More... »

PAGES

33-72

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-0348-0903-0_2

DOI

http://dx.doi.org/10.1007/978-3-0348-0903-0_2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1011428654


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