{"paper":{"title":"Shadowing and Hyperbolicity for Endomorphisms of Locally Compact Groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Dekui Peng","submitted_at":"2026-06-26T01:56:46Z","abstract_excerpt":"We study the shadowing property for continuous endomorphisms of locally compact groups, using the left uniformity. For Lie groups we obtain a complete infinitesimal characterization: an endomorphism has shadowing if and only if its differential is hyperbolic. As consequences, positively expansive Lie group endomorphisms are automatically topologically expanding, and for Lie group automorphisms, expansiveness, shadowing, two-sided shadowing and being topologically Anosov are equivalent. We also show that, for connected semisimple Lie groups, shadowing endomorphisms are precisely nilpotent endom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27647","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27647/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}