{
  "id": "2306.06575",
  "version": "v1",
  "published": "2023-06-11T03:44:32.000Z",
  "updated": "2023-06-11T03:44:32.000Z",
  "title": "Finiteness of physical measures for diffeomorphisms with multi 1-D centers",
  "authors": [
    "Yongluo Cao",
    "Zeya Mi"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be a $C^2$ diffeomorphism on compact Riemannian manifold $M$ with partially hyperbolic splitting $$ TM=E^u\\oplus E_1^c\\oplus\\cdots\\oplus E_k^c \\oplus E^s, $$ where $E^u$ is uniformly expanding, $E^s$ is uniformly contracting, and ${\\rm dim}E_i^c=1,~ 1\\le i \\le k, ~k\\ge 1$. We prove the finiteness of ergodic physical(SRB) measures of $f$ under the hyperbolicity of Gibbs $u$-states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-11T03:44:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C40",
      "37D25",
      "37D30"
    ],
    "keywords": [
      "physical measures",
      "finiteness",
      "diffeomorphism",
      "compact riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}