• Corpus ID: 119330293

Weak Gibbs and Equilibrium Measures for Shift Spaces

@article{Pfister2019WeakGA,
  title={Weak Gibbs and Equilibrium Measures for Shift Spaces},
  author={C. E. Pfister and Wayne G. Sullivan},
  journal={arXiv: Dynamical Systems},
  year={2019}
}
For a large class of irreducible shift spaces $X\subset\tA^{\Z^d}$, with $\tA$ a finite alphabet, and for absolutely summable potentials $\Phi$, we prove that equilibrium measures for $\Phi$ are weak Gibbs measures. In particular, for $d=1$, the result holds for irreducible sofic shifts. 
1 Citations
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Let (X,T) be a dynamical system, where X is a compact metric space and T a continuous onto map. For weak Gibbs measures we prove large deviations estimates.
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Ergodic theory concerns with the study of the long-time behavior of a dynamical system. An interesting result known as Birkhoff’s ergodic theorem states that under certain conditions, the time