{"paper":{"title":"Robustly transitive behavior in symplectic dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Under a domination condition, real-analytic deformations of the product of a symplectomorphism with a basic set and one with a non-degenerate elliptic equilibrium produce large robustly transitive sets.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jaime Paradela","submitted_at":"2026-05-15T13:05:11Z","abstract_excerpt":"We consider the direct product of two symplectomorphisms, one of which exhibits a basic set and the other one a non-degenerate elliptic equilibrium. Under a domination condition we show that a broad class of real-analytic deformations of this system display large robustly transitive sets. As a corollary of our construction we also obtain new examples of real-analytic robustly transitive symplectomorphisms which are not uniformly hyperbolic.\n  To establish these results we develop perturbation techniques to create blender horseshoes in the real-analytic setting and import ideas from control the"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under a domination condition we show that a broad class of real-analytic deformations of this system display large robustly transitive sets. As a corollary we also obtain new examples of real-analytic robustly transitive symplectomorphisms which are not uniformly hyperbolic.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The domination condition between the basic set of the first symplectomorphism and the non-degenerate elliptic equilibrium of the second, which is invoked to guarantee that the blender horseshoes created by perturbation have a sufficiently large domain of influence.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Under a domination condition, real-analytic deformations of symplectomorphism products yield large robustly transitive sets and new non-uniformly-hyperbolic examples via blender-horseshoe perturbations and control-theory ideas.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Under a domination condition, real-analytic deformations of the product of a symplectomorphism with a basic set and one with a non-degenerate elliptic equilibrium produce large robustly transitive sets.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"dbddc3461f7164f9a1213de2371a0a6d2a88709e5ba1fb16665d6f0a10351233"},"source":{"id":"2605.15922","kind":"arxiv","version":1},"verdict":{"id":"c62c85f8-80de-48d4-b25f-b9c06191e6b9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:13:11.592549Z","strongest_claim":"Under a domination condition we show that a broad class of real-analytic deformations of this system display large robustly transitive sets. As a corollary we also obtain new examples of real-analytic robustly transitive symplectomorphisms which are not uniformly hyperbolic.","one_line_summary":"Under a domination condition, real-analytic deformations of symplectomorphism products yield large robustly transitive sets and new non-uniformly-hyperbolic examples via blender-horseshoe perturbations and control-theory ideas.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The domination condition between the basic set of the first symplectomorphism and the non-degenerate elliptic equilibrium of the second, which is invoked to guarantee that the blender horseshoes created by perturbation have a sufficiently large domain of influence.","pith_extraction_headline":"Under a domination condition, real-analytic deformations of the product of a symplectomorphism with a basic set and one with a non-degenerate elliptic equilibrium produce large robustly transitive sets."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15922/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.056444Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:21:19.775343Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:46.551276Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.750357Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6b2f342d17e9b0e4c6ae5f83689f9a583b3bf34ab450c56554e344734e815271"},"references":{"count":110,"sample":[{"doi":"","year":2025,"title":"Partially hyperbolic dynamics in the 3-body problem , author=. 2025 , eprint=","work_id":"a2ab7aca-f086-4307-9cc3-643f2f80ee1f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1215/00127094-2022-0073","year":2023,"title":"Clarke, A. and Turaev, D. , TITLE =. 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