{
  "id": "1008.2329",
  "version": "v1",
  "published": "2010-08-13T14:30:12.000Z",
  "updated": "2010-08-13T14:30:12.000Z",
  "title": "Embedding of global attractors and their dynamics",
  "authors": [
    "Eleonora Pinto de Moura",
    "James C. Robinson",
    "Jaime J. Sánchez-Gabites"
  ],
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "abstract": "Using shape theory and the concept of cellularity, we show that if $A$ is the global attractor associated with a dissipative partial differential equation in a real Hilbert space $H$ and the set $A-A$ has finite Assouad dimension $d$, then there is an ordinary differential equation in ${\\mathbb R}^{m+1}$, with $m >d$, that has unique solutions and reproduces the dynamics on $A$. Moreover, the dynamical system generated by this new ordinary differential equation has a global attractor $X$ arbitrarily close to $LA$, where $L$ is a homeomorphism from $A$ into ${\\mathbb R}^{m+1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-13T14:30:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global attractor",
      "ordinary differential equation",
      "dissipative partial differential equation",
      "real hilbert space",
      "finite assouad dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.2329P"
    }
  }
}