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arXiv · 2411.15050

Anisotropic spaces for the bilateral shift

Mateus Marra·Daniel Smania
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Abstract

Given two Hölder potentials $ϕ_+$ and $ψ_-$ for the unilateral shift, we define anisotropic Banach spaces of distributions on the bilateral shift space with a finite alphabet. On these spaces, the transfer operator for the bilateral shift is quasicompact with a spectral gap, and the unique Gibbs state associated with $ϕ_+$ spans its $1$-eigenspace. This result allows us to establish exponential decay of correlations for Hölder observables and a wide range of measures on the bilateral shift space.

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Mateus Marra, Daniel Smania. 2025-12-18. Anisotropic spaces for the bilateral shift. https://doi.org/10.1007/s10884-025-10474-y

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