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Massive evaluation and analysis of Poincaré recurrences

Ivan I. Shevchenko; Guillaume Rollin; Alexander V. Melnikov; José Lages


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{
  "publisher": "Zenodo", 
  "DOI": "10.5281/zenodo.3228905", 
  "language": "eng", 
  "title": "Massive evaluation and analysis of Poincar\u00e9 recurrences", 
  "issued": {
    "date-parts": [
      [
        2019, 
        5, 
        25
      ]
    ]
  }, 
  "abstract": "<p>We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar&eacute; recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. This new method allows one to construct, in some approximation, charts of local diffusion timescales.</p>", 
  "author": [
    {
      "family": "Ivan I. Shevchenko"
    }, 
    {
      "family": "Guillaume Rollin"
    }, 
    {
      "family": "Alexander V. Melnikov"
    }, 
    {
      "family": "Jos\u00e9 Lages"
    }
  ], 
  "type": "article", 
  "id": "3228905"
}
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