{
  "id": "2309.09144",
  "version": "v1",
  "published": "2023-09-17T03:25:30.000Z",
  "updated": "2023-09-17T03:25:30.000Z",
  "title": "Exponential rate of decay of correlations of equilibrium states associated with non-uniformly expanding circle maps",
  "authors": [
    "Eduardo Garibaldi",
    "Irene Inoquio-Renteria"
  ],
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "In the context of expanding maps of the circle with an indifferent fixed point, understanding the joint behavior of dynamics and pairs of moduli of continuity $ (\\omega, \\Omega) $ may be a useful element for the development of equilibrium theory. Here we identify a particular feature of modulus $ \\Omega $ (precisely $ \\lim_{x \\to 0^+} \\sup_{\\mathsf d} \\Omega\\big({\\mathsf d} x \\big) / \\Omega(\\mathsf d) = 0 $) as a sufficient condition for the system to exhibit exponential decay of correlations with respect to the unique equilibrium state associated with a potential having $ \\omega $ as modulus of continuity. This result is derived from obtaining the spectral gap property for the transfer operator acting on the space of observables with $ \\Omega $ as modulus of continuity, a property that, as is well known, also ensures the Central Limit Theorem. Examples of application of our results include the Manneville-Pomeau family",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-17T03:25:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-uniformly expanding circle maps",
      "exponential rate",
      "correlations",
      "unique equilibrium state",
      "continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}