{"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"}