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

Scott Schmieding

Research output: Contribution to journalArticlepeer-review

Abstract

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)
Pages (from-to)2552-2570
Number of pages19
JournalErgodic Theory and Dynamical Systems
Volume40
Issue number9
DOIs
StatePublished - Sep 1 2020

Keywords

  • Lyapunov exponents
  • automorphism
  • entropy
  • shift of finite type

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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