Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-08T17:34:40.415Z Has data issue: false hasContentIssue false
  • English
  • Français

Block maps between primitive uniform and Pisot substitutions

Published online by Cambridge University Press:  04 August 2014

VILLE SALO Open the ORCID record for VILLE SALO [Opens in a new window]  and
ILKKA TÖRMÄ
VILLE SALO
Affiliation:
TUCS – Turku Centre for Computer Science, University of Turku, Finland email vosalo@utu.fi, iatorm@utu.fi
ILKKA TÖRMÄ
Affiliation:
TUCS – Turku Centre for Computer Science, University of Turku, Finland email vosalo@utu.fi, iatorm@utu.fi
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, we prove that for all pairs of primitive Pisot or uniform substitutions with the same dominating eigenvalue, there exists a finite set of block maps such that every block map between the corresponding subshifts is an element of this set, up to a shift.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 7 , October 2015 , pp. 2292 - 2310
Copyright
© Cambridge University Press, 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adamczewski, B.. Symbolic discrepancy and self-similar dynamics. Ann. Inst. Fourier 54 (2004), 2201–2234.CrossRefGoogle Scholar
Boyle, M. and Tomiyama, J.. Bounded topological orbit equivalence and C ∗ -algebras. J. Math. Soc. Japan 50(2) (1998), 317–329.CrossRefGoogle Scholar
Coven, E. M., Dykstra, A., Keane, M. and LeMasurier, M.. Necessary and sufficient conditions for a dynamical system to be topologically conjugate to a given substitution minimal system. ArXiv e-prints, June 2013.Google Scholar
Coven, E. M.. Endomorphisms of substitution minimal sets. Probab. Theory Related Fields 20(2) (1971), 129–133.Google Scholar
Coven, E. M., Keane, M. and LeMasurier, M.. A characterization of the morse minimal set up to topological conjugacy. Ergod. Th. & Dynam. Sys. 28 (2008), 1443–1451.CrossRefGoogle Scholar
Durand, F., Host, B. and Skau, C.. Substitutional dynamical systems, Bratteli diagrams and dimension groups. Ergod. Th. & Dynam. Sys. 19(4) (1999), 953–993.CrossRefGoogle Scholar
Durand, F.. Linearly recurrent subshifts have a finite number of non-periodic subshift factors. Ergod. Th. & Dynam. Sys. 20 (2000), 1061–1078.CrossRefGoogle Scholar
Giordano, T., Putnam, I. F. and Skau, C. F.. Topological orbit equivalence and C ∗ -crossed products. J. Reine Angew. Math. 469 (1995), 51–111.Google Scholar
Giordano, T., Putnam, I. F. and Skau, C. F.. Cocycles for cantor minimal ℤd -systems. Int. J. Math. 20(9) (2009), 1107–1135.CrossRefGoogle Scholar
Harju, T. and Linna, M.. On the periodicity of morphisms on free monoids. RAIRO Inform. Théor. Appl. 20(1) (1986), 47–54.CrossRefGoogle Scholar
Host, B. and Parreau, F.. Homomorphismes entre systèmes dynamiques définis par substitutions. Ergod. Th. & Dynam. Sys. 9 (1989), 469–477.CrossRefGoogle Scholar
Mossé, B.. Puissances de mots et reconnaissabilité des points fixes d’une substitution. Theoret. Comput. Sci. 99(2) (1992), 327–334.CrossRefGoogle Scholar
Mossé, B.. Reconnaissabilité des substitutions et complexité des suites automatiques. Bull. Soc. Math. France 124(2) (1996), 329–346.CrossRefGoogle Scholar
Olli, J.. Endomorphisms of sturmian systems and the discrete chair substitution tiling system. Dyn. Sys. 33(9) (2013), 4173–4186.Google Scholar
Pansiot, J.-J.. Decidability of periodicity for infinite words. RAIRO Inform. Théor. Appl. 20(1) (1986), 43–46.CrossRefGoogle Scholar
Queffélec, M.. Substitution Dynamical Systems—Spectral Analysis (Lecture Notes in Mathematics, 1294). Springer, Berlin, 1987.CrossRefGoogle Scholar