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Suppose that the dynamical system $(X,G)$ is expansive and is the quotient by a uniformly bounded-to-one factor map of a strongly irreducible subshift. Let $\\tau \\colon X \\to X$ be a continuous map commuting with the action of $G$. We prove that if there is no pair of distinct $G$-homoclinic points in $X$ having the same image under $\\tau$, then $\\tau$ is surjective."},"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":"1508.07553","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T10:57:32Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d70d7707e8628883c88daecf0adb9258f9a9dff8dfb66e9560adf2ec7367b9e6","abstract_canon_sha256":"c27b16c5333071d09f71e5203a4240a0fa4a0e94bca8b021b1a3e7f3a911e690"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:00.101095Z","signature_b64":"yWOZ3JBOTrQPwW6qjxeNwCgxKMfPnQyFtrC/UPTOKTTUUllf9zingzKl79NitR84lSq8dXMDgN8axBLVX/uRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"798e3b3ba5b939480d4588b55aee33339e6442f27e32abe61c26eaf842a79d84","last_reissued_at":"2026-05-18T01:04:00.100451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:00.100451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Expansive actions of countable amenable groups, homoclinic pairs, and the Myhill property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Michel Coornaert, Tullio Ceccherini-Silberstein","submitted_at":"2015-08-30T10:57:32Z","abstract_excerpt":"Let $X$ be a compact metrizable space equipped with a continuous action of a countable amenable group $G$. 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