Skip to main content

Eigenvalues of Substitution Dynamical Systems

Part of the Lecture Notes in Mathematics book series (LNM,volume 1294)

Abstract

This chapter is devoted to the description of eigenvalues of the dynamical system (X,μ,T) arising from a primitive and aperiodic substitution ζ. We distinguish the case of constant-length substitutions from the case of nonconstant-length ones. In the first case, the result is due to M. Dekking [68] and J.C. Martin [174] who made use of a different approach. The description of the eigenvalues in the general case has been essentially established by B. Host [119]. Another reformulation and a new proof, in somewhat more geometric terms, have been given ten years later [87] and we just outline the ideas. The third part raises the problem of pure point spectrum for substitution dynamical systems, with emphasize on the emblematic Pisot case.

Keywords

  • Pure Point Spectrum
  • Generalize Eigenfunction
  • Coincidence Condition
  • Equivalent Pair
  • Primitive Substitution

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   59.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   79.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Martine Queffélec .

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Queffélec, M. (2010). Eigenvalues of Substitution Dynamical Systems. In: Substitution Dynamical Systems - Spectral Analysis. Lecture Notes in Mathematics(), vol 1294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11212-6_6

Download citation