Cocycles with Quasi-Conformality I: Stability and abundance
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| Format: | Preprint |
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2024
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| _version_ | 1866913626028244992 |
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| author | Nassiri, Meysam Rajabzadeh, Hesam Reshadat, Zahra |
| author_facet | Nassiri, Meysam Rajabzadeh, Hesam Reshadat, Zahra |
| contents | This is the first part of a series of papers devoted to the study of linear cocycles over chaotic systems. In the present paper, we establish the existence of such cocycles that $\mathcal{C}^α$-stably exhibit fiberwise bounded orbits ($α>0$). The proof is based on a new mechanism which yields stable elliptic-type behavior in $\mathrm{GL}(d,\mathbb{R})$ or $\mathrm{SL}(d,\mathbb{R})$ cocycles. Moreover, we show that this phenomenon is $\mathcal{C}^0$-dense among $\mathrm{SL}(d,\mathbb{R})$ cocycles over a shift of finite type without dominated splitting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_13921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cocycles with Quasi-Conformality I: Stability and abundance Nassiri, Meysam Rajabzadeh, Hesam Reshadat, Zahra Dynamical Systems 37C20, 37D30 (Primary) 37A20, 37D25, 37D20 (Secondary) This is the first part of a series of papers devoted to the study of linear cocycles over chaotic systems. In the present paper, we establish the existence of such cocycles that $\mathcal{C}^α$-stably exhibit fiberwise bounded orbits ($α>0$). The proof is based on a new mechanism which yields stable elliptic-type behavior in $\mathrm{GL}(d,\mathbb{R})$ or $\mathrm{SL}(d,\mathbb{R})$ cocycles. Moreover, we show that this phenomenon is $\mathcal{C}^0$-dense among $\mathrm{SL}(d,\mathbb{R})$ cocycles over a shift of finite type without dominated splitting. |
| title | Cocycles with Quasi-Conformality I: Stability and abundance |
| topic | Dynamical Systems 37C20, 37D30 (Primary) 37A20, 37D25, 37D20 (Secondary) |
| url | https://arxiv.org/abs/2408.13921 |