Approximations of symbolic substitution systems in one dimension
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914914521579520 |
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| author | Tenenbaum, Lior |
| author_facet | Tenenbaum, Lior |
| contents | Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schrödinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra approximate the spectrum of the limiting operator (of the quasicrystal). This naturally leads to study the convergence of the underlying dynamical systems. We treat dynamical systems which are based on one-dimensional substitutions. We first find natural candidates of dynamical subsystems to approximate the substitution dynamical system. Subsequently, we offer a characterization of their convergence and provide estimates for the rate of convergence. We apply the proposed theory to some guiding examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19151 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximations of symbolic substitution systems in one dimension Tenenbaum, Lior Dynamical Systems Mathematical Physics Spectral Theory 52C23, 37B10, 37B52, 81Q10 Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schrödinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra approximate the spectrum of the limiting operator (of the quasicrystal). This naturally leads to study the convergence of the underlying dynamical systems. We treat dynamical systems which are based on one-dimensional substitutions. We first find natural candidates of dynamical subsystems to approximate the substitution dynamical system. Subsequently, we offer a characterization of their convergence and provide estimates for the rate of convergence. We apply the proposed theory to some guiding examples. |
| title | Approximations of symbolic substitution systems in one dimension |
| topic | Dynamical Systems Mathematical Physics Spectral Theory 52C23, 37B10, 37B52, 81Q10 |
| url | https://arxiv.org/abs/2402.19151 |