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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2602.08147 |
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| _version_ | 1866912888761876480 |
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| author | Rastegar, Reza |
| author_facet | Rastegar, Reza |
| contents | This paper studies structured products of real matrices for which the top Lyapunov exponent can be accessed by reducing the dynamics to an amenable generalization of upper triangular matrices. Exploiting prescribed zero patterns (including block-triangularity and sparse decompositions, conveniently encoded by a directed sparsity graph), we obtain explicit, computable bounds and, in favorable cases, formulas for $γ_1$ by combining deterministic triangular controls with a suitable refinement of the Furstenberg--Kifer lemma for block-triangular products. The estimates apply both to tempered (possibly deterministic) sequences and to stationary ergodic random cocycles under standard integrability. We also discuss applications to perturbation models for linear systems, including low-rank updates, where the reduction converts the problem to lower-dimensional or scalar cocycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08147 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lyapunov Exponents for Sparsely Coupled Linear Cocycles Rastegar, Reza Dynamical Systems Mathematical Physics Probability 37H15, 37M25 This paper studies structured products of real matrices for which the top Lyapunov exponent can be accessed by reducing the dynamics to an amenable generalization of upper triangular matrices. Exploiting prescribed zero patterns (including block-triangularity and sparse decompositions, conveniently encoded by a directed sparsity graph), we obtain explicit, computable bounds and, in favorable cases, formulas for $γ_1$ by combining deterministic triangular controls with a suitable refinement of the Furstenberg--Kifer lemma for block-triangular products. The estimates apply both to tempered (possibly deterministic) sequences and to stationary ergodic random cocycles under standard integrability. We also discuss applications to perturbation models for linear systems, including low-rank updates, where the reduction converts the problem to lower-dimensional or scalar cocycles. |
| title | Lyapunov Exponents for Sparsely Coupled Linear Cocycles |
| topic | Dynamical Systems Mathematical Physics Probability 37H15, 37M25 |
| url | https://arxiv.org/abs/2602.08147 |