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It is known that BS(1,n) is isomorphic to the group generated by the two affine maps of the real line: $f_0(x) = x + 1$ and $h_0(x) = nx $.\n  This paper deals with the dynamics of actions of BS(1,n) on closed orientable surfaces. We exhibit a smooth BS(1,n) action without finite orbits on $\\TT ^2$, we study the dynamical behavior of it and of its $C^1$-pertubations and we prove that it is not locally rigid.\n  We develop a general dynamical study for faithful topological BS(1,n)-actions on clo"},"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":"1004.2126","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-13T09:19:50Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"811e7752e65d1a3bbbd344028c1f531b2ef8aedb60a5a3f00182eea60a83cc9a","abstract_canon_sha256":"0111bf5ca3667d6c43e03a7250e64ec6a825314e0410a7c532dfd237ae6715a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:04.579889Z","signature_b64":"WLDEGBocdkMIYRu3CJGIRqlI5XRfmeeTZ8MjfdOM1kROl2J36e0PqZCVa8EUVpfoEh1DaIfVN85VsMPygV+dCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8fc7545b60594ca91e698f1ba33e5abb70c501b92ae8ef39ec647021e787bd8","last_reissued_at":"2026-05-18T04:15:04.579244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:04.579244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Actions of Baumslag-Solitar groups on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Isabelle Liousse, Nancy Guelman","submitted_at":"2010-04-13T09:19:50Z","abstract_excerpt":"Let $BS(1,n) =< a, b \\ | \\ aba^{-1} = b^n >$ be the solvable Baumslag-Solitar group, where $ n\\geq 2$. It is known that BS(1,n) is isomorphic to the group generated by the two affine maps of the real line: $f_0(x) = x + 1$ and $h_0(x) = nx $.\n  This paper deals with the dynamics of actions of BS(1,n) on closed orientable surfaces. We exhibit a smooth BS(1,n) action without finite orbits on $\\TT ^2$, we study the dynamical behavior of it and of its $C^1$-pertubations and we prove that it is not locally rigid.\n  We develop a general dynamical study for faithful topological BS(1,n)-actions on clo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2126","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1004.2126","created_at":"2026-05-18T04:15:04.579373+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.2126v2","created_at":"2026-05-18T04:15:04.579373+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2126","created_at":"2026-05-18T04:15:04.579373+00:00"},{"alias_kind":"pith_short_12","alias_value":"7D6HKRNWAWKM","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"7D6HKRNWAWKMVEPG","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"7D6HKRNW","created_at":"2026-05-18T12:26:04.259169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7D6HKRNWAWKMVEPGTDY3UM7FVO","json":"https://pith.science/pith/7D6HKRNWAWKMVEPGTDY3UM7FVO.json","graph_json":"https://pith.science/api/pith-number/7D6HKRNWAWKMVEPGTDY3UM7FVO/graph.json","events_json":"https://pith.science/api/pith-number/7D6HKRNWAWKMVEPGTDY3UM7FVO/events.json","paper":"https://pith.science/paper/7D6HKRNW"},"agent_actions":{"view_html":"https://pith.science/pith/7D6HKRNWAWKMVEPGTDY3UM7FVO","download_json":"https://pith.science/pith/7D6HKRNWAWKMVEPGTDY3UM7FVO.json","view_paper":"https://pith.science/paper/7D6HKRNW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.2126&json=true","fetch_graph":"https://pith.science/api/pith-number/7D6HKRNWAWKMVEPGTDY3UM7FVO/graph.json","fetch_events":"https://pith.science/api/pith-number/7D6HKRNWAWKMVEPGTDY3UM7FVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7D6HKRNWAWKMVEPGTDY3UM7FVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7D6HKRNWAWKMVEPGTDY3UM7FVO/action/storage_attestation","attest_author":"https://pith.science/pith/7D6HKRNWAWKMVEPGTDY3UM7FVO/action/author_attestation","sign_citation":"https://pith.science/pith/7D6HKRNWAWKMVEPGTDY3UM7FVO/action/citation_signature","submit_replication":"https://pith.science/pith/7D6HKRNWAWKMVEPGTDY3UM7FVO/action/replication_record"}},"created_at":"2026-05-18T04:15:04.579373+00:00","updated_at":"2026-05-18T04:15:04.579373+00:00"}