An infinite-dimensional version of the Poincaré-Birkhoff theorem on the Hilbert cube

• Alberto Boscaggin ^[3] ; Alessandro Fonda ^[1] ; Maurizio Garrione ^[2]
  1. [1] University of Trieste

     University of Trieste

     Trieste, Italia

     
  2. [2] Polytechnic University of Milan

     Polytechnic University of Milan

     Milán, Italia

     
  3. [3] Università di Torino, Italia

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 20, Nº 2, 2020, págs. 751-770
• Idioma: inglés
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• Resumen

  • We propose a version of the Poincare´–Birkhoff theorem for infinitedimensional Hamiltonian systems, which extends a recent result by Fonda and Uren˜a [20]. The twist condition, adapted to a Hilbert cube, is spread on a sequence of approximating finite-dimensional systems. Some applications are proposed to pendulum-like systems of infinitely many ODEs. We also extend to the infinite-dimensional setting a celebrated theorem by Conley and Zehnder [9].