{
  "annotation_id": "adbb5d53-b4e6-4f21-82f3-e483ee9a3b08",
  "date_created": "2026-03-02T18:00:47.005000Z",
  "date_modified": "2026-03-02T18:00:47.005000Z",
  "file_hash": "677e0f35573cea32f5a9457df28cc8fd8a4e9399607c970d25f9a0d3b1a8fd95",
  "private": false,
  "record": {
    "abstract": "For slowly evolving, discrete-time-dependent systems of difference equations\n(iterated maps), we believe the simplest means of demonstrating the validity of\nthe averaging method at first order is by way of a lemma that we call Besjes\u0027\ninequality. In this paper, we develop the Besjes inequality for identity maps\nwith perturbations that are (i) at low-order resonance (periodic with short\nperiod) and (ii) far from low-order resonance in the discrete time. We use\nthese inequalities to prove corresponding first-order averaging principles,\ntogether with a principle of adiabatic invariance on extended timescales; and\nwe generalize and apply these mathematical results to model problems in\naccelerator beam dynamics, and to the Henon map.",
    "arxiv_id": "physics/0311058",
    "authors": [
      "Scott Dumas",
      "James A. Ellison",
      "Mathias Vogt"
    ],
    "categories": [
      "physics.acc-ph",
      "math.DS"
    ],
    "title": "First-Order Averaging Principles for Maps with Applications to Beam   Dynamics in Particle Accelerators",
    "url": "https://arxiv.org/abs/physics/0311058"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "280970a5-c695-433b-88e5-1efcdd82caf4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}