{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VE4I7Q3H2ERURDLT6REWS3UDG2","short_pith_number":"pith:VE4I7Q3H","schema_version":"1.0","canonical_sha256":"a9388fc367d123488d73f449696e8336b4cf70b74b98a98f1cd9e2324893c859","source":{"kind":"arxiv","id":"1906.07486","version":1},"attestation_state":"computed","paper":{"title":"Dynamic of generalized transvections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guido Ahumada (IRIMAS), Nicolas Chevallier (IRIMAS)","submitted_at":"2019-06-18T10:32:07Z","abstract_excerpt":"Given an increasing odd homeomorphism $\\sigma$ : R $\\rightarrow$ R, the two bijective maps h $\\sigma$ , v $\\sigma$ : R 2 $\\rightarrow$ R 2 dened by h $\\sigma$ (x, y) = (x + $\\sigma$ --1 (y), y) and v $\\sigma$ (x, y) = (x, $\\sigma$(x) + y). are called generalized transvections. We study the action on the plane of the group $\\Gamma$($\\sigma$) generated by these two maps. Particularly interesting cases arise when $\\sigma$(x) = sgn(x)|x| $\\alpha$. We prove that most points have dense orbits and that every nonzero point has a dense orbit when $\\sigma$(x) = sgn(x)|x| 2. We also look at invariant mea"},"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":"1906.07486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-18T10:32:07Z","cross_cats_sorted":[],"title_canon_sha256":"da2f57f19db8def19a0efeadb345fcedbdc60ab5af0a2c357ab217151c164be8","abstract_canon_sha256":"7112594c3cc394fa4d09f12416c7144bafd865bf58572c2e2c0f22a60618d9aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:07.802152Z","signature_b64":"Dm8KYDZE8/ld7w8LlRIKjluQQ4FKF4fcSicRk5uxE6UnDVASy1zKgfz14wrn9dq0nzfGbAh83nVsFDBzveA7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9388fc367d123488d73f449696e8336b4cf70b74b98a98f1cd9e2324893c859","last_reissued_at":"2026-05-17T23:43:07.801546Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:07.801546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamic of generalized transvections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guido Ahumada (IRIMAS), Nicolas Chevallier (IRIMAS)","submitted_at":"2019-06-18T10:32:07Z","abstract_excerpt":"Given an increasing odd homeomorphism $\\sigma$ : R $\\rightarrow$ R, the two bijective maps h $\\sigma$ , v $\\sigma$ : R 2 $\\rightarrow$ R 2 dened by h $\\sigma$ (x, y) = (x + $\\sigma$ --1 (y), y) and v $\\sigma$ (x, y) = (x, $\\sigma$(x) + y). are called generalized transvections. We study the action on the plane of the group $\\Gamma$($\\sigma$) generated by these two maps. Particularly interesting cases arise when $\\sigma$(x) = sgn(x)|x| $\\alpha$. We prove that most points have dense orbits and that every nonzero point has a dense orbit when $\\sigma$(x) = sgn(x)|x| 2. We also look at invariant mea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07486","kind":"arxiv","version":1},"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":"1906.07486","created_at":"2026-05-17T23:43:07.801630+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.07486v1","created_at":"2026-05-17T23:43:07.801630+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07486","created_at":"2026-05-17T23:43:07.801630+00:00"},{"alias_kind":"pith_short_12","alias_value":"VE4I7Q3H2ERU","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"VE4I7Q3H2ERURDLT","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"VE4I7Q3H","created_at":"2026-05-18T12:33:30.264802+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/VE4I7Q3H2ERURDLT6REWS3UDG2","json":"https://pith.science/pith/VE4I7Q3H2ERURDLT6REWS3UDG2.json","graph_json":"https://pith.science/api/pith-number/VE4I7Q3H2ERURDLT6REWS3UDG2/graph.json","events_json":"https://pith.science/api/pith-number/VE4I7Q3H2ERURDLT6REWS3UDG2/events.json","paper":"https://pith.science/paper/VE4I7Q3H"},"agent_actions":{"view_html":"https://pith.science/pith/VE4I7Q3H2ERURDLT6REWS3UDG2","download_json":"https://pith.science/pith/VE4I7Q3H2ERURDLT6REWS3UDG2.json","view_paper":"https://pith.science/paper/VE4I7Q3H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.07486&json=true","fetch_graph":"https://pith.science/api/pith-number/VE4I7Q3H2ERURDLT6REWS3UDG2/graph.json","fetch_events":"https://pith.science/api/pith-number/VE4I7Q3H2ERURDLT6REWS3UDG2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VE4I7Q3H2ERURDLT6REWS3UDG2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VE4I7Q3H2ERURDLT6REWS3UDG2/action/storage_attestation","attest_author":"https://pith.science/pith/VE4I7Q3H2ERURDLT6REWS3UDG2/action/author_attestation","sign_citation":"https://pith.science/pith/VE4I7Q3H2ERURDLT6REWS3UDG2/action/citation_signature","submit_replication":"https://pith.science/pith/VE4I7Q3H2ERURDLT6REWS3UDG2/action/replication_record"}},"created_at":"2026-05-17T23:43:07.801630+00:00","updated_at":"2026-05-17T23:43:07.801630+00:00"}