{
  "id": "2105.03739",
  "version": "v1",
  "published": "2021-05-08T16:52:04.000Z",
  "updated": "2021-05-08T16:52:04.000Z",
  "title": "Persistence of Heterodimensional Cycles",
  "authors": [
    "Dongchen Li",
    "Dmitry Turaev"
  ],
  "comment": "64 pages, 5 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "A heterodimensional cycle is an invariant set of a dynamical system consisting of two hyperbolic periodic orbits with different dimensions of their unstable manifolds and a pair of orbits that connect them. For systems which are at least C^2, we show that bifurcations of a coindex-1 heterodimensional cycle within a generic 2-parameter family always create robust heterodimensional dynamics, i.e., chain-transitive sets which contain coexisting orbits with different numbers of positive Lyapunov exponents and persist for an open set of parameter values. In particular, we solve the so-called $C^r$-stabilization problem for the coindex-1 heterodimensional cycles in any regularity class $r=2,\\ldots,\\infty,\\omega$. The results are based on the observation that arithmetic properties of moduli of topological conjugacy of systems with heterodimensional cycles determine the emergence of Bonatti-D\\'iaz blenders.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-08T16:52:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C05",
      "37C20",
      "37C25",
      "37C29",
      "37G25"
    ],
    "keywords": [
      "persistence",
      "create robust heterodimensional dynamics",
      "hyperbolic periodic orbits",
      "heterodimensional cycles determine",
      "open set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}