{"paper":{"title":"Lower Bounds for non-Archimedean Lyapunov Exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Kenneth Jacobs","submitted_at":"2015-10-08T18:50:58Z","abstract_excerpt":"Let $K$ be a complete, algebraically closed, non-Archimedean valued field, and let $\\textbf{P}^1$ denote the Berkovich projective line over $K$. The Lyapunov exponent for a rational map $\\phi\\in K(z)$ of degree $d\\geq 2$ measures the exponential rate of growth along a typical orbit of $\\phi$. When $\\phi$ is defined over $\\mathbb{C}$, the Lyapunov exponent is bounded below by $\\frac{1}{2}\\log d$. In this article, we give a lower bound for $L(\\phi)$ for maps $\\phi$ defined over non-Archimedean fields $K$. The bound depends only on the degree $d$ and the Lipschitz constant of $\\phi$. For maps $\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02440","kind":"arxiv","version":3},"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"}