---
res:
  bibo_abstract:
  - 'A bifurcation is a qualitative change in a family of solutions to an equation
    produced by varying parameters. In contrast to the local bifurcations of dynamical
    systems that are often related to a change in the number or stability of equilibria,
    bifurcations of boundary value problems are global in nature and may not be related
    to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed
    framework which studies the bifurcations of critical points of functions. In this
    paper we study the bifurcations of solutions of boundary-value problems for symplectic
    maps, using the language of (finite-dimensional) singularity theory. We associate
    certain such problems with a geometric picture involving the intersection of Lagrangian
    submanifolds, and hence with the critical points of a suitable generating function.
    Within this framework, we then study the effect of three special cases: (i) some
    common boundary conditions, such as Dirichlet boundary conditions for second-order
    systems, restrict the possible types of bifurcations (for example, in generic
    planar systems only the A-series beginning with folds and cusps can occur); (ii)
    integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic
    pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing
    symmetries can exhibit restricted bifurcations associated with the symmetry. This
    approach offers an alternative to the analysis of critical points in function
    spaces, typically used in the study of bifurcation of variational problems, and
    opens the way to the detection of more exotic bifurcations than the simple folds
    and cusps that are often found in examples. @eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Robert I
      foaf_name: McLachlan, Robert I
      foaf_surname: McLachlan
  - 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
  bibo_doi: 10.1088/1361-6544/aab630
  dct_date: 2018^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0951-7715
  - http://id.crossref.org/issn/1361-6544
  dct_language: eng
  dct_title: Bifurcation of solutions to Hamiltonian boundary value problems@
...