{"paper":{"title":"Lyapunov exponents for products of matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Chiu-Hong Lo, De-Jun Feng, Shuang Shen","submitted_at":"2017-02-23T15:07:49Z","abstract_excerpt":"Let ${\\bf M}=(M_1,\\ldots, M_k)$ be a tuple of real $d\\times d$ matrices. Under certain irreducibility assumptions, we give checkable criteria for deciding whether ${\\bf M}$ possesses the following property: there exist two constants $\\lambda\\in {\\Bbb R}$ and $C>0$ such that for any $n\\in {\\Bbb N}$ and any $i_1, \\ldots, i_n \\in \\{1,\\ldots, k\\}$, either $M_{i_1} \\cdots M_{i_n}={\\bf 0}$ or $C^{-1} e^{\\lambda n} \\leq \\| M_{i_1} \\cdots M_{i_n} \\| \\leq C e^{\\lambda n}$, where $\\|\\cdot\\|$ is a matrix norm. The proof is based on symbolic dynamics and the thermodynamic formalism for matrix products. As"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07251","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}