Automorphisms of the shift: Lyapunov exponents, entropy, and the dimension representation

S. C.O.T.T. Schmieding*

*Corresponding author for this work

Research output: Contribution to journalArticle


Let be a shift of finite type and its corresponding automorphism group. Associated to are certain Lyapunov exponents, which describe asymptotic behavior of the sequence of coding ranges of. We give lower bounds on in terms of the spectral radius of the corresponding action of on the dimension group associated to. We also give lower bounds on the topological entropy in terms of a distinguished part of the spectrum of the action of on the dimension group, but show that, in general, is not bounded below by the logarithm of the spectral radius of the action of on the dimension group.

Original languageEnglish (US)
JournalErgodic Theory and Dynamical Systems
Publication statusPublished - Jan 1 2019



  • 2010 Mathematics Subject Classification
  • 37B10 (Primary)

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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