{
  "id": "2103.03847",
  "version": "v1",
  "published": "2021-03-05T18:01:33.000Z",
  "updated": "2021-03-05T18:01:33.000Z",
  "title": "Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems",
  "authors": [
    "Qinbo Chen",
    "Rafael de la Llave"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "nlin.CD"
  ],
  "abstract": "We study the problem of instability in the following a priori unstable Hamiltonian system with a time-periodic perturbation \\[\\mathcal{H}_\\varepsilon(p,q,I,\\varphi,t)=h(I)+\\sum_{i=1}^n\\pm \\left(\\frac{1}{2}p_i^2+V_i(q_i)\\right)+\\varepsilon H_1(p,q,I,\\varphi, t), \\] where $(p,q)\\in \\mathbb{R}^n\\times\\mathbb{T}^n$, $(I,\\varphi)\\in\\mathbb{R}^d\\times\\mathbb{T}^d$ with $n, d\\geq 1$, $V_i$ are Morse potentials, and $\\varepsilon$ is a small non-zero parameter. Using geometric methods we prove that Arnold diffusion occurs for generic analytic perturbations $H_1$. Indeed, the set of admissible $H_1$ is $C^\\omega$ dense and $C^3$ open. The proof also works for arbitrarily small $V_i$. Our perturbative technique for the genericity is valid in the $C^k$ topology for all $k\\in [3,\\infty)\\cup\\{\\infty, \\omega\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-05T18:01:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J40",
      "37J25",
      "70H08",
      "70H33"
    ],
    "keywords": [
      "priori unstable hamiltonian system",
      "analytic genericity",
      "diffusing orbits",
      "arnold diffusion occurs",
      "small non-zero parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}