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 language | English (US) |
|---|---|
| Pages (from-to) | 2552-2570 |
| Number of pages | 19 |
| Journal | Ergodic Theory and Dynamical Systems |
| Volume | 40 |
| Issue number | 9 |
| DOIs | |
| State | Published - Sep 1 2020 |
Funding
Acknowledgement. This research was supported in part by the National Science Foundation grant ‘RTG: Analysis on manifolds’ at Northwestern University. I would like to thank Ville Salo for communicating to us the example in Remark 4.8, and Masakazu Nasu for referring me to results contained in his article [22]. I am especially grateful to Mike Boyle for many helpful discussions and comments.
Keywords
- Lyapunov exponents
- automorphism
- entropy
- shift of finite type
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics