Renato Calleja, Jordi-Llu s Figueras
Collision of invariant bundles of 
quasi-periodic attractors in the dissipative 
standard map
(1789K, pdf)

ABSTRACT.  We perform a numerical study of the breakdown of hyperbolicity of quasi-periodic 
attractors in the dissipative standard map. In this study, we compute the quasi- 
periodic attractors together with their stable and tangent bundles. We observe that 
the loss of normal hyperbolicity comes from the collision of the stable and tangent 
bundles of the quasi-periodic attractor. We provide numerical evidence that, close to 
the breakdown, the angle between the invariant bundles has a linear behavior with 
respect to the perturbing parameter. This linear behavior agrees with the universal 
asymptotics of the general framework of breakdown of hyperbolic quasi-periodic tori 
in skew product systems.