{
  "abstract": "We develop a geometric stability framework for dynamical systems coupled to memory fields generated by their own state trajectories. Temporal age and state-space displacement enter a nonlinear hereditary force admitting an exact, trajectory-dependent velocity representation. A common velocity-history phase space contains both resting and uniformly translating solutions. We establish global velocity arrest under a uniform geometric memory-gain bound and obtain exact translating-speed balance laws from the full radial imprint. The response slope yields a positive longitudinal exponent on rising-speed branches, while a complementary contraction criterion gives local exponential attraction to selected descending branches in the scalar velocity dynamics, in fading-memory topology. Our principal result is a constructive geometric non-identifiability theorem: two systems with identical nonlinear force operators on an open neighborhood of rest can exhibit sharply different complete-motion behavior at the same subcritical gain. In the first, every admissible trajectory with bounded velocity prehistory comes to rest exponentially; in the second, locally attracting rest coexists with a locally attracting translating branch and an additional spectrally unstable translating branch. The infinite-memory case exhibits exponentially flat force differences, with all finite-order equilibrium derivatives agreeing despite the possibility of distinct global translating families. The framework also yields classical Volterra kernels and distributed-derivative transfer functions by linearization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24152",
  "author_total": 1,
  "authors": [
    {
      "name": "Robert Vrabel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25vcqmc22s102.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24152",
  "fulltext_url": null,
  "id": "25vcqmc22s102",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24152",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7223004742",
  "pdf_url": "https://arxiv.org/pdf/2610.24152",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25vcqmc22s102.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24152",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24152"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Geometric Stability of Dynamical Systems with Self-Generated State-Space Memory",
  "title_text": "Geometric Stability of Dynamical Systems with Self-Generated State-Space Memory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/25vcqmc22s102",
  "venue": "arXiv",
  "versions": []
}