Lyapunov spectrum via boundary theory I
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913791732613120 |
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| author | Bader, Uri Furman, Alex |
| author_facet | Bader, Uri Furman, Alex |
| contents | This paper is concerned with the Lyapunov spectrum for measurable cocycles
over an ergodic pmp system taking values in semi-simple real Lie groups.
We prove simplicity of the Lyapunov spectrum and its continuity
under certain perturbations for a class systems that includes many
familiar examples.
Our framework uses some soft qualitative assumptions, and does not
rely on symbolic dynamics.
We use ideas from boundary theory
that appear in the study of super-rigidity to deduce our results.
This gives a new perspective even on the most studied case of random
matrix products.
The current paper introduces the general framework and contains the proofs
of the main results and some basic examples.
In a follow up paper we discuss further examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09731 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lyapunov spectrum via boundary theory I Bader, Uri Furman, Alex Dynamical Systems Group Theory This paper is concerned with the Lyapunov spectrum for measurable cocycles over an ergodic pmp system taking values in semi-simple real Lie groups. We prove simplicity of the Lyapunov spectrum and its continuity under certain perturbations for a class systems that includes many familiar examples. Our framework uses some soft qualitative assumptions, and does not rely on symbolic dynamics. We use ideas from boundary theory that appear in the study of super-rigidity to deduce our results. This gives a new perspective even on the most studied case of random matrix products. The current paper introduces the general framework and contains the proofs of the main results and some basic examples. In a follow up paper we discuss further examples. |
| title | Lyapunov spectrum via boundary theory I |
| topic | Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2504.09731 |