Automorphisms of the shift

Lyapunov exponents, entropy, and the dimension representation

Scott Edward Schmieding*

*Corresponding author for this work

Research output: Contribution to journalArticle

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)
JournalErgodic Theory and Dynamical Systems
DOIs
StatePublished - Jan 1 2019

Fingerprint

Representation Dimension
Dimension Group
Lyapunov Exponent
Automorphisms
Entropy
Spectral Radius
Shift of Finite Type
Lower bound
Topological Entropy
Logarithm
Automorphism Group
Coding
Asymptotic Behavior
Range of data

Keywords

  • 2010 Mathematics Subject Classification
  • 37B10 (Primary)

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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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.",
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author = "Schmieding, {Scott Edward}",
year = "2019",
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language = "English (US)",
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Automorphisms of the shift : Lyapunov exponents, entropy, and the dimension representation. / Schmieding, Scott Edward.

In: Ergodic Theory and Dynamical Systems, 01.01.2019.

Research output: Contribution to journalArticle

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Y1 - 2019/1/1

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AB - 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.

KW - 2010 Mathematics Subject Classification

KW - 37B10 (Primary)

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