Another look at the saddle-centre bifurcation: Vanishing Twist
Holger Dullin
Loughborough University
The most fundamental bifurcation is the creation of a pair of
periodic orbits 'out of nothing'. In area preserving maps this is
called the saddle-centre bifurcation, in which an elliptic and a
hyperbolic orbit are born.
The twist condition in KAM theory requires that the rotation number
of neighboring invariant curves changes. I will first review the interesting
dynamical consequences of vanishing twist, and then explain the main result:
The twist vanishes before the creation of the pair of saddle-centre orbits.
Thus, 'out of nothing' should be replaced by 'out of a twistless curve'.
The area preserving Henon map will serve as an example of this
general principle.