---
res:
  bibo_abstract:
  - "Ordinary differential equations (ODEs) and partial differential equations (PDEs)
    arise\r\nin most scientific disciplines that make use of mathematical techniques.
    As exact solutions are in general not computable, numerical methods are used to
    obtain approximate\r\nsolutions. In order to draw valid conclusions from numerical
    computations, it is crucial\r\nto understand which qualitative aspects numerical
    solutions have in common with the\r\nexact solution. Symplecticity is a subtle
    notion that is related to a rich family of geometric properties of Hamiltonian
    systems. While the effects of preserving symplecticity\r\nunder discretisation
    on long-term behaviour of motions is classically well known, in this\r\nthesis\r\n(a)
    the role of symplecticity for the bifurcation behaviour of solutions to Hamiltonian\r\nboundary
    value problems is explained. In parameter dependent systems at a bifurcation\r\npoint
    the solution set to a boundary value problem changes qualitatively. Bifurcation\r\nproblems
    are systematically translated into the framework of classical catastrophe theory.
    It is proved that existing classification results in catastrophe theory apply
    to\r\npersistent bifurcations of Hamiltonian boundary value problems. Further
    results for\r\nsymmetric settings are derived.\r\n(b) It is proved that to preserve
    generic bifurcations under discretisation it is necessary and sufficient to preserve
    the symplectic structure of the problem.\r\n(c) The catastrophe theory framework
    for Hamiltonian ODEs is extended to PDEs\r\nwith variational structure. Recognition
    equations for A-series singularities for functionals on Banach spaces are derived
    and used in a numerical example to locate high-codimensional bifurcations.\r\n(d)
    The potential of symplectic integration for infinite-dimensional Lie-Poisson systems
    (Burgers’ equation, KdV, fluid equations, . . . ) using Clebsch variables is analysed.\r\nIt
    is shown that the advantages of symplectic integration can outweigh the disadvantages
    of integrating over a larger phase space introduced by a Clebsch representation.\r\n(e)
    Finally, the preservation of variational structure of symmetric solutions in multisymplectic
    PDEs by multisymplectic integrators on the example of (phase-rotating)\r\ntravelling
    waves in the nonlinear wave equation is discussed.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Christian
      foaf_name: Offen, Christian
      foaf_surname: Offen
      foaf_workInfoHomepage: http://www.librecat.org/personId=85279
    orcid: https://orcid.org/0000-0002-5940-8057
  dct_date: 2020^xs_gYear
  dct_language: eng
  dct_publisher: Massey University@
  dct_title: Analysis of Hamiltonian boundary value problems and symplectic integration@
...