Peeling bifurcations of toroidal chaotic attractors.
Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated peeling bifurcations, describe their topological structures and the changes undergone as a symmetry axis crosses the original attractor, and indicate how the symbol name of a trajectory in the original lifts to one in the cover. Covering orbits are described using a powerful synthesis of kneading theory with refinements of the circle map. These methods are applied to a simple version of the van der Pol oscillator.
Letellier
Christophe
C
CORIA UMR 6614--Université de Rouen, Av. de l'Université, Boîte Postale 12, F-76801 Saint-Etienne du Rouvray cedex, France.
Gilmore
Robert
R
Jones
Timothy
T