Lyapunov spectrum rigidity and simultaneous linearization for random Anosov diffeomorphisms
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914240135168000 |
|---|---|
| author | Brown, Aaron Shi, Yi |
| author_facet | Brown, Aaron Shi, Yi |
| contents | In this paper we study the Lyapunov spectrum rigidity for random walks of expanding maps on unit circle $\mathbb{S}^1$ and Anosov diffeomorphisms on $d$-torus $\mathbb{T}^d$. Let $ν$ be a probability supported on the set of expanding maps on $\mathbb{S}^1$ or a neighborhood of a generic Anosov automorphisms on $\mathbb{T}^d$. If the Lyapunov spectrum of the $ν$-stationary SRB-measure coincides with the Lyapunov spectrum of the algebraic action, then we can simultaneously linearize $ν$ almost every system to an affine action. Moreover, we prove the positive Lyapunov exponent rigidity for random walks of irreducible positive matrices acting on $\mathbb{T}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04679 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lyapunov spectrum rigidity and simultaneous linearization for random Anosov diffeomorphisms Brown, Aaron Shi, Yi Dynamical Systems In this paper we study the Lyapunov spectrum rigidity for random walks of expanding maps on unit circle $\mathbb{S}^1$ and Anosov diffeomorphisms on $d$-torus $\mathbb{T}^d$. Let $ν$ be a probability supported on the set of expanding maps on $\mathbb{S}^1$ or a neighborhood of a generic Anosov automorphisms on $\mathbb{T}^d$. If the Lyapunov spectrum of the $ν$-stationary SRB-measure coincides with the Lyapunov spectrum of the algebraic action, then we can simultaneously linearize $ν$ almost every system to an affine action. Moreover, we prove the positive Lyapunov exponent rigidity for random walks of irreducible positive matrices acting on $\mathbb{T}^2$. |
| title | Lyapunov spectrum rigidity and simultaneous linearization for random Anosov diffeomorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2601.04679 |