{
  "id": "2407.05373",
  "version": "v1",
  "published": "2024-07-07T13:55:38.000Z",
  "updated": "2024-07-07T13:55:38.000Z",
  "title": "Monotonicity of the set of zeros of the Lyapunov exponent with respect to shift embeddings",
  "authors": [
    "Oleg Safronov"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the discrete Schr\\\"odinger operators with potentials whose values are read along the orbits of a shift of finite type. We study a certain subset of the collection of energies at which the Lyapunov exponent is zero and prove monotonicity of this set with respect to the shift embeddings. Then we introduce a certain function ${\\mathcal J}(A,\\mu)$ determined by the position of these zeros and prove monotonicity of ${\\mathcal J}(A,\\mu)$ with respect to embeddings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-07T13:55:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34L05"
    ],
    "keywords": [
      "lyapunov exponent",
      "shift embeddings",
      "monotonicity",
      "finite type",
      "potentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}