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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.11848 |
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| _version_ | 1866909035540774912 |
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| author | Nassiri, Meysam Rajabzadeh, Hesam Reshadat, Zahra |
| author_facet | Nassiri, Meysam Rajabzadeh, Hesam Reshadat, Zahra |
| contents | As the second part of a series on linear cocycles over chaotic systems, this paper establishes a "multiple covering principle" that robustly yields positive-entropy ergodic measures supported on fiberwise uniformly bounded orbits. Using this mechanism, we prove that any continuous $\mathrm{SL}(d,\mathbb{R})$ cocycle over a positive-entropy subshift of finite type either admits a dominated splitting or can be $C^0$-approximated by one that $C^α$-stably supports such measures ($α>0$). Additionally, for non-isometric cocycles, we show that the topological entropy of these bounded orbits is strictly less than that of the base subshift. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11848 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cocycles with Quasi-Conformality II: Ergodic measures with positive entropy Nassiri, Meysam Rajabzadeh, Hesam Reshadat, Zahra Dynamical Systems As the second part of a series on linear cocycles over chaotic systems, this paper establishes a "multiple covering principle" that robustly yields positive-entropy ergodic measures supported on fiberwise uniformly bounded orbits. Using this mechanism, we prove that any continuous $\mathrm{SL}(d,\mathbb{R})$ cocycle over a positive-entropy subshift of finite type either admits a dominated splitting or can be $C^0$-approximated by one that $C^α$-stably supports such measures ($α>0$). Additionally, for non-isometric cocycles, we show that the topological entropy of these bounded orbits is strictly less than that of the base subshift. |
| title | Cocycles with Quasi-Conformality II: Ergodic measures with positive entropy |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.11848 |