Parameter spaces of locally constant cocycles
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| Accesso online: | |
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| _version_ | 1866918100264288256 |
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| author | Christodoulou, Argyrios |
| author_facet | Christodoulou, Argyrios |
| contents | This article concerns the locus of all locally constant $\mathrm{SL}(2,\mathbb{R})$-valued cocycles that are uniformly hyperbolic, called the hyperbolic locus. Using the theory of semigroups of Möbius transformations we introduce a new locus in $\mathrm{SL}(2,\mathbb{R})^N$ which allows us to study the complement of the hyperbolic locus. Our results answer a question of Avila, Bochi and Yoccoz, and Jacques and Short, while motivating a new line of investigation on the subject. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_14511 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Parameter spaces of locally constant cocycles Christodoulou, Argyrios Dynamical Systems 37D20 (Primary), 30F45 (Secondary) This article concerns the locus of all locally constant $\mathrm{SL}(2,\mathbb{R})$-valued cocycles that are uniformly hyperbolic, called the hyperbolic locus. Using the theory of semigroups of Möbius transformations we introduce a new locus in $\mathrm{SL}(2,\mathbb{R})^N$ which allows us to study the complement of the hyperbolic locus. Our results answer a question of Avila, Bochi and Yoccoz, and Jacques and Short, while motivating a new line of investigation on the subject. |
| title | Parameter spaces of locally constant cocycles |
| topic | Dynamical Systems 37D20 (Primary), 30F45 (Secondary) |
| url | https://arxiv.org/abs/2009.14511 |