Mathematical remarks on transcritical bifurcation in Hamiltonian systems

@inproceedings{JnichMathematicalRO,
title={Mathematical remarks on transcritical bifurcation in Hamiltonian systems},
author={K. J{\"a}nich}
}

K. Jänich

This article is meant as a mathematical appendix or comment on [1]. We first consider the notion of transcritical bifurcations of fixed points of general area-preserving maps, and then adress some questions related to [1] on bifurcation in Poincaré maps of 2-dimensional Hamiltonian systems. 1 Rank-1-bifurcations Let differentiable (C ∞) functions Q = Q(q, p, ε) and P = P (q, p, ε) be defined on an open neighborhood of the origin in (q, p, ε)-space R 3. We assume (P, Q) to be symplectic in the… CONTINUE READING