Anisotropic spaces for the bilateral shift
| Title: | Anisotropic spaces for the bilateral shift |
|---|---|
| Authors: | Marra, Mateus, Smania, Daniel |
| Publication Year: | 2024 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Dynamical Systems, Mathematics - Analysis of PDEs, Mathematics - Functional Analysis, 37A25, 37A30, 37A46, 37C30, 37D05, 37D35, 37D20, 43A85, 47B37, 43A15, 46E36, 46F99 |
| More Details: | Given two H\"older potentials $\phi_+$ and $\psi_-$ 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 $\phi_+$ spans its $1$-eigenspace. This result allows us to establish exponential decay of correlations for H\"older observables and a wide range of measures on the bilateral shift space. Comment: 34 pages, 1 figure |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2411.15050 |
| Accession Number: | edsarx.2411.15050 |
| Database: | arXiv |
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