Random 2D linear cocycles I: dichotomic behavior
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917968739303424 |
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| author | Duarte, Pedro Durães, Marcelo Graxinha, Tomé Klein, Silvius |
| author_facet | Duarte, Pedro Durães, Marcelo Graxinha, Tomé Klein, Silvius |
| contents | In this paper we establish a Bochi-Mañé type dichotomy in the space of two dimensional, nonnegative determinant matrix valued, locally constant linear cocycles over a Bernoulli or Markov shift. Moreover, we prove that Lebesgue almost every such cocycle has finite first Lyapunov exponent, which then implies a break in the regularity of the Lyapunov exponent, from analyticity to discontinuity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random 2D linear cocycles I: dichotomic behavior Duarte, Pedro Durães, Marcelo Graxinha, Tomé Klein, Silvius Dynamical Systems Mathematical Physics 37H15 In this paper we establish a Bochi-Mañé type dichotomy in the space of two dimensional, nonnegative determinant matrix valued, locally constant linear cocycles over a Bernoulli or Markov shift. Moreover, we prove that Lebesgue almost every such cocycle has finite first Lyapunov exponent, which then implies a break in the regularity of the Lyapunov exponent, from analyticity to discontinuity. |
| title | Random 2D linear cocycles I: dichotomic behavior |
| topic | Dynamical Systems Mathematical Physics 37H15 |
| url | https://arxiv.org/abs/2503.21050 |