{"paper":{"title":"Dynamical Systems as Functorial Realisations of Abstract Evolution Shapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CT","authors_text":"Bangxin Wang","submitted_at":"2026-07-20T01:06:04Z","abstract_excerpt":"We develop a categorical framework for closed dynamical systems in which the abstract pattern of admissible evolutions is separated from its concrete realisation. A closed dynamical system is formulated as a functor $X\\colon S\\to C$ from a small category $S$, viewed as an abstract evolution shape, to a coefficient category $C$. By varying $S$ and $C$, this single definition encompasses many important examples including autonomous, non-autonomous, switched, hybrid, and stochastic systems. Within this framework, we introduce invariant subsystems, equilibria, and orbits in functorial terms. We th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17455","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/2607.17455/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"}