A periodically forced flow displaying symmetry breaking via a three-tori gluing bifurcation and two-tori resonances

The dynamics due to a periodic forcing (harmonic axial oscillations) in a T aylor-Couette apparatus of finite length is examined numerically in an axis ymmetric subspace. The forcing delays the onset of centrifugal instability and introduces a Z(2) symmetry that involves both space and time. This pape r examines the influence of this symmetry on the subsequent bifurcations an d route to chaos in a one-dimensional path through parameter space as the c entrifugal instability is enhanced. We have observed a well-known route to chaos via frequency locking and torus break-up on a two-tori branch once th e Z(2) symmetry has been broken. However, this branch is not connected in a simple manner to the Z(2)-invariant primary branch. An intermediate branch of three-tori solutions, exhibiting heteroclinic and homoclinic bifurcatio ns, provides the connection. On this three-tori branch, a new gluing bifurc ation of three-tori is seen to play a central role in the symmetry breaking process. (C) 2001 Elsevier Science B.V. All rights reserved.