  This article is meant as a mathematical appendix or comment on [BT]. We first
consider the notion of transcritical bifurcations of fixed points of general
area-preserving maps, and then adress some questions related to [BT] on
bifurcation in Poincar\'e maps of 2-dimensional Hamiltonian systems.
  [BT] M. Brack and K. Tanaka, arXiv:0705.0753
