{"paper":{"title":"Salem numbers in dynamics of K\\\"ahler threefolds and complex tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.AG","authors_text":"Keiji Oguiso, Tuyen Trung Truong","submitted_at":"2013-09-19T04:33:08Z","abstract_excerpt":"Let $X$ be a compact K\\\"ahler manifold of dimension $k\\leq 4$ and $f:X\\rightarrow X$ a pseudo-automorphism. If the first dynamical degree $\\lambda_1(f)$ is a Salem number, we show that either $\\lambda_1(f)=\\lambda_{k-1}(f)$ or $\\lambda_1(f)^2=\\lambda_{k-2}(f)$. In particular, if $\\mbox{dim}(X)=3$ then $\\lambda_1(f)=\\lambda_2(f)$. We use this to show that if $X$ is a complex 3-torus and $f$ is an automorphism of $X$ with $\\lambda_1(f)>1$, then $f$ has a non-trivial equivariant holomorphic fibration if and only if $\\lambda_1(f)$ is a Salem number. If $X$ is a complex 3-torus having an automorphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4851","kind":"arxiv","version":2},"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"}