2015
AUTHORSS. Akiyama , M. Barge , V. Berthé , J.-Y. Lee , A. Siegel
ABSTRACTOur 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... »
PAGES33-72
Mathematics of Aperiodic Order
ISBN
978-3-0348-0902-3
978-3-0348-0903-0
http://scigraph.springernature.com/pub.10.1007/978-3-0348-0903-0_2
DOIhttp://dx.doi.org/10.1007/978-3-0348-0903-0_2
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