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@PHDTHESIS{Masci:1002419,
      author       = {Masci, Leonardo},
      othercontributors = {Hryniewicz, Umberto and Abbondandolo, Alberto},
      title        = {{A}bundance of periodic orbits in asymptotically linear
                      {H}amiltonian systems},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2025-00518},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2025},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2025},
      abstract     = {In this thesis a twist condition which applies to
                      asymptotically linear Hamiltonian diffeomorphisms of linear
                      phase space is introduced. This twist condition is inspired
                      by the classical Poincaré-Birkhoff theorem on
                      area-preserving maps of the annulus. The main goal of the
                      thesis is to use the twist condition to find periodic points
                      of asymptotically linear Hamiltonian diffeomorphisms.
                      Namely, it is shown that if an asymptotically linear
                      Hamiltonian diffeomorphism, which is non-degenerate and
                      unitary at infinity, satisfies the twist condition, then it
                      must have infinitely many periodic points. To prove this
                      theorem, a construction of Floer homology for asymptotically
                      linear Hamiltonian diffeomorphisms is provided, and a
                      technique to relate the filtered Floer homologies of
                      different iterates of the same asymptotically linear
                      Hamiltonian diffeomorphism is introduced.},
      cin          = {112710 / 110000},
      ddc          = {510},
      cid          = {$I:(DE-82)112710_20190828$ / $I:(DE-82)110000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2025-00518},
      url          = {https://publications.rwth-aachen.de/record/1002419},
}