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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.4851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-19T04:33:08Z","cross_cats_sorted":["math.CV","math.DS"],"title_canon_sha256":"09feef71863e607bc84a2b337ca2aeb37698bd3c71b305c60b1599182b6d36b3","abstract_canon_sha256":"034a7aa06b6740a1d74dce50e6969010d0bc983114597cb33b45c7df9bb8100d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:26.517589Z","signature_b64":"axmGwMLBdT1mift5H88tHJFDKVSDI+6zcbE1ez84ZYbGijE7ADyR1k8eFrjYDbHztSv/1LY8LAiFkj1uPNKgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19574bbb0502ba09e87523bcd69782081cfb125cfa3e8f8044cba8a698460c96","last_reissued_at":"2026-05-18T02:57:26.516916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:26.516916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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