Mathematical remarks on transcritical bifurcation in Hamiltonian systems

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