Scaling laws for bubbling bifurcations

We establish rigorous scaling laws for the average bursting time for bubbling bifurcations of an invariant manifold, assuming the dynamics within the manifold to be uniformly hyperbolic. This type of global bifurcation appears in nearly synchronized systems, and is conjectured to be typical among those breaking the invariance of an asymptotically stable hyperbolic invariant manifold. We consider bubbling precipitated by generic bifurcations of a fixed point in both symmetric and non-symmetric systems with a codimension one invariant manifold, and discuss their extension to bifurcations of periodic points. We also discuss generalizations to invariant manifolds with higher codimension, and to systems with random noise.